Multi-beam exposer unit

ABSTRACT

A multi-beam exposer unit  1  includes          ∑     i   =   1     M          (     Ni   -   1     )                     
     half mirror  11  for synthesizing          ∑     i   =   1     M        Ni                   
     light to M groups of light beams, M sets of optical members  12 , having positive power with a large absolute value as compared with a case of a main scanning direction, for further converging the beam in a sub-scanning direction, a synthesizing reflection mirror  13  for reflecting M groups of beams to be substantially overlaid on each other in a first direction, a polygon mirror unit  5  for deflecting M groups of beams, and a dust prevention glass  14  inclined to a direction opposite to a direction where the half mirror is inclined, thereby reducing influence of coma aberration exerted on M groups of beams by the half mirror.

This application is a divisional of application Ser. No. 09/468,546,filed Dec. 21, 1999, which is in turn a divisional of Ser. No.09/903,943, filed Jul. 31, 1997 now U.S. Pat. No. 6,100,912.

BACKGROUND OF THE INVENTION

The present invention relates to a multi-beam exposer unit, which isused in a color printer device of a plurality of drums type, a colorcopy machine of a plurality of drums type, a multi-color printer, amulti-color copy machine, a monochromatic high-speed laser printer, amonochromatic high-speed digital copy machine, for scanning a pluralityof beams.

For example, in an image forming device such as a color printer or acolor copy machine, there are used a plurality of image forming units,and a laser exposer unit or an optical scanning device, which providesimage data corresponding to color components, which are color-separated,that is, a plurality of laser beams to the image forming units.

The exposer unit has a first lens group, an optical deflector, and asecond lens group. The first lens group reduces a cross-sectional beamdiameter of a laser beam emitted from a semiconductor laser element to apredetermined size. The optical deflector is used to continuouslydeflect the laser beam reduced by the first lens group to a directionperpendicular to a direction where a recording medium is transferred.The second lens group is used to image-form the laser beam deflected bythe optical deflector at a predetermined position of the recordingmedium. In many cases, a direction where the laser beam is deflected bythe optical deflector is shown as a main scanning direction. Then, adirection where the recording medium is transferred, that is, adirection, which is perpendicular to the main scanning direction, isshown as a sub-scanning direction.

As this type of the exposer unit, the following examples are known:

Specifically, a plurality of optical scanning devices are arranged tocorrespond to the respective image forming sections in order to adjustto the image forming device to be applied. Also, a multi-beam exposerunit, which is formed to be capable of providing a plurality of laserbeams.

In the following explanation, the direction of the rotational axis ofthe deflector is called as a sub-scanning direction. Also, thedirection, which is perpendicular to the direction of the optical axisof the optical system and that of the rotational axis of the deflector,is called as a main scanning direction. In the image forming device, thesub-scanning direction of the optical system corresponds to the transferdirection of the transfer material. The main scanning direction showsthe direction, which is perpendicular to the transfer direction in thesurface of the transfer material. Also, in the following explanation,the image surface is a transfer material surface, and the image-formedsurface is a surface where the beam is actually formed.

For example, there is an optical system comprising M sets of lightsources, a pre-deflection optical system, serving as first opticalmeans, and a post-deflection optical system serving as second opticalmeans. The light sources emit Ni light beams, and at least one set ofthe light sources satisfies Ni≧2. The pre-deflection optical systemincludes a plurality of finite focal lenses, a half mirror, which is$\sum\limits_{i = 1}^{M}\left( {{Ni} - 1} \right)$

first synthetic reflection mirrors, a cylinder lens, which is M sets ofoptical materials, and M−1 second synthetic reflection mirrors. Thefinite focal lenses convert light emitted from the light source toconvergent light. The half mirror puts together emission light from therespective finite focal lenses as one light beam in which the emissionlight is substantially overlaid on each other. Then, one light beam issynthesized to be M beam groups. The half mirror reflects apredetermined percentage of incident light and transmits a predeterminedpercentage of incident light. To further converge the light beams, whichare synthesized to be M beam groups in the sub-scanning direction, thecylinder lens is provided with positive power having an absolute valuelarger than in the main scanning direction. The second syntheticreflection mirrors reflect M beam groups from the cylinder lens to besubstantially overlaid on each other in the first direction.

The post-deflection optical system includes a polygon mirror, serving asone deflection means, and a pair of fθ lens. The polygon mirror hasreflected surfaces formed to be rotatable and to deflect light in apredetermined direction. The fθ lens image-forms$\sum\limits_{i = 1}^{M}{Ni}$

beams deflected by the polygon mirror (deflection means) on apredetermined image surface to be scanned at an equal speed, andcorrects influence caused by a difference between inclinations of therespective reflection surfaces of the polygon mirror.

To make the transmitting convergent light beam incident obliquely on thehalf mirror, the beam transmitting through the first syntheticreflection mirror generates a variation of a focal length, a sphericalaberration, a coma aberration, and astigmatism.

If the thickness of the half mirror, a refractive index, and an incidentangle are t, n, and u, respectively, the amount of each of the variationof a focal length, a spherical aberration, a coma aberration, andastigmatism can be shown as follows:

Variation of focal length: (t×(1−1/n))

Spherical aberration: Bi=−t×u⁴×(n²−1)/n³

Coma aberration: Fi=−t×u³×(n²−1)/n³

Astigmatism: Ci=−t×u²×(n²−1)/n²

In this case, the variation of the focal length can be completelycanceled by increasing a length of an optical path between the finitelens and a hybrid cylinder lens by t×(1−1/n).

Regarding the spherical aberration, the distance between the finite lensand the cylinder lens, and the length of the optical path between thecylinder lens and the polygon mirror reflected point are suitably setsuch that the image surface can be moved to the center of the positionwhere the peripheral light beam of each of the respective main scanningand sub-scanning directions intersects at the main light beam. Thereby,influence caused by the spherical aberration can be reduced.

Regarding astigmatism, the length of the optical path between the finitelens and the cylinder lens, and the length of the optical path betweenthe cylinder length and the polygon mirror reflected point are suitablyset, so that astigmatism can be completely canceled.

However, regarding the coma aberration, no correction method is proposedso far, and influence is exerted on a characteristic of theimage-formation at the image surface.

In the optical system having no aberration, if the laser beam having abeam waist diameter of ω0 is defocused by z, the beam waist diameter ofω can be obtained by the following equation:

ω=ω₀(1+(λz/(πω₀ ²))²)½  (A)

where λ is a wavelength.

In other words, if the amount of defocus is z, the beam diameter changesfrom ω0 to ω. Due to the variation of the beam diameter, the thicknessof the lines of the image and image density are varied.

It is assumed that fθ lens is formed of a plastic lens separately fromthe above structure.

In this case, if the lens is separated from the image surface to reducethe size of the optical system itself, the amount of defocus of thesub-scanning direction is varied by the change in temperature andhumidity. In this case, the beam position of the main scanning directionis varied.

BRIEF SUMMARY OF THE INVENTION

An object of the present invention is to reduce the influence in comaaberration of a multi-beam exposer unit scanning a plurality of beams.

According to a first aspect of the prevent invention, there is provideda multi-beam exposer unit comprising:

M sets of light sources for emitting Ni (i=1−M) light beams wherein atleast one set of the light sources satisfies i≧2;

first optical means including a plurality of finite focal lenses forconverting light beams emitted from the respective light sources toconvergent light, $\sum\limits_{i = 1}^{M}\left( {{Ni} - 1} \right)$

 first synthesizing reflection mirror for reflecting a predeterminedrate of incident light and transmitting a predetermined rate of incidentlight so as to synthesize light to M groups of beams passing through thefinite focal lenses, thereby combining $\sum\limits_{i = 1}^{M}{Ni}$

 emission light from the respective finite focal lenses as one beam, Msets of optical members, having positive power with a large absolutevalue as compared with a case of a main scanning direction, for furtherconverging the beam in a sub-scanning direction, and M−1 secondsynthesizing reflection mirror for reflecting M groups of beams from Msets of optical members to be substantially overlaid on each other in afirst direction;

deflecting means, having reflection surfaces formed to be rotatable, fordeflecting light to a predetermined direction;

second optical means having lenses for image-forming$\sum\limits_{i = 1}^{M}{Ni}$

 beams on a predetermined image surface at an equal speed, and forcorrecting an inclination of the deflecting means; and

a parallel plate provided in an optical path between the light sourceand the deflecting means to be inclined to a side opposite to the firstsynthesizing reflection mirror, seeing from the light beam transmittingthrough the first synthesizing reflection mirror.

According to the second aspect of the prevent invention, there isprovided a multi-beam exposer unit comprising:

at least light sources and an image forming optical system, wherein animage forming position provided by the image forming optical system isplaced such that a beam passing through a portion close to a main beamis defined to be a light source side than an image surface, and that abeam passing through a portion close to an outermost beam is defined tobe a side away from the light source seeing from the image surface.

According to the third aspect of the prevent invention, there isprovided a multi-beam exposer unit comprising:

M sets of light sources for emitting Ni (i=1−M) light beams;

first optical means including a plurality of finite focal lenses forconverting light beams emitted from the respective light sources toconvergent light, $\sum\limits_{i = 1}^{M}\left( {{Ni} - 1} \right)$

 first synthesizing reflection mirror for reflecting a predeterminedrate of incident light and transmitting a predetermined rate of incidentlight so as to synthesize M groups of beams passing through the finitefocal lenses, thereby combining $\sum\limits_{i = 1}^{M}{Ni}$

 emission light from the respective finite focal lenses as one beam, Msets of optical members, having positive power with a large absolutevalue as compared with a case of a main scanning direction, for furtherconverging the beam in a sub-scanning direction, and M−1 secondsynthesizing reflection mirror for reflecting M groups of beams from Msets of optical members to be substantially overlaid on each other in afirst direction;

deflecting means, having reflection surfaces formed to be rotatable, fordeflecting light to a predetermined direction;

second optical means having two plastic lenses for image-forming$\sum\limits_{i = 1}^{M}{Ni}$

 beams on a predetermined image surface at an equal speed, and forcorrecting an inclination of the deflecting means, wherein the twoplastic lenses include an image forming characteristic of one lensshowing that each of the two lens is positioned such that a distancefrom a reflection point on the deflecting means is shorter than adistance from the an image surface, one plastic lens placed on the sideof the deflecting means side has a function of moving an image formingposition to the side of the deflecting means at a portion close to thecenter of the lens, and moving the image forming position of thescanning direction to a side opposite to the deflecting means at aportion close to the lens end portion.

According to the fourth aspect of the prevent invention, there isprovided a multi-beam exposer unit comprising:

M sets of light sources for emitting one Ni (i=1−M) light beams;

first optical means including a plurality of finite focal lenses forconverting light beams emitted from the respective light sources toconvergent light, $\sum\limits_{i = 1}^{M}\left( {{Ni} - 1} \right)$

 first synthesizing reflection mirror for reflecting a predeterminedrate of incident light and transmitting a predetermined rate of incidentlight so as to synthesize M groups of beams passing through the finitefocal lenses, thereby combining $\sum\limits_{i = 1}^{M}{Ni}$

 emission light from the respective finite focal lenses as one beam, Msets of optical members, having positive power with a large absolutevalue as compared with a case of a main scanning direction, for furtherconverging the beam in a sub-scanning direction, and M−1 secondsynthesizing reflection mirror for reflecting M groups of beams from Msets of optical members to be substantially overlaid on each other in afirst direction;

deflecting means, having reflection surfaces formed to be rotatable, fordeflecting light to a predetermined direction;

second optical means having two plastic lenses for image-forming$\sum\limits_{i = 1}^{M}{Ni}$

 beams on a predetermined image surface at an equal speed, and forcorrecting an inclination of the deflecting means, wherein each of thetwo plastic lenses is positioned to include an image formingcharacteristic showing that a distance from a reflection point on thedeflecting means is shorter than a distance from the image surface, oneplastic lens placed on the side of the deflecting means side has afunction of moving an image forming position of a scanning direction andan image forming position of a perpendicular direction to the side ofthe deflecting means seeing from the image surface at a portion close tothe center of the lens.

According to the fifth aspect of the prevent invention, there isprovided a multi-beam exposer unit comprising:

M sets of light sources for emitting Ni (i=1−M) light beams;

first optical means including a plurality of finite focal lenses forconverting light beams emitted from the respective light sources toconvergent light, $\sum\limits_{i = 1}^{M}\left( {{Ni} - 1} \right)$

 first synthesizing reflection mirror for reflecting a predeterminedrate of incident light and transmitting a predetermined rate of incidentlight so as to synthesize M groups of beams passing through the finitefocal lenses, thereby combining $\sum\limits_{i = 1}^{M}{Ni}$

 emission light from the respective finite focal lenses as one beam, Msets of optical members, having positive power with a large absolutevalue as compared with a case of a main scanning direction, for furtherconverging the beam in a sub-scanning direction, and M−1 secondsynthesizing reflection mirror for reflecting M groups of beams from Msets of optical members to be substantially overlaid on each other in afirst direction;

deflecting means, having reflection surfaces formed to be rotatable, fordeflecting light to a predetermined direction;

second optical means having two plastic lenses for image-forming$\sum\limits_{i = 1}^{M}{Ni}$

 beams on a predetermined image surface at an equal speed, and forcorrecting an inclination of the deflecting means, wherein each of thetwo plastic lenses is positioned to include an image formingcharacteristic showing that a distance from a reflection point on thedeflecting means is shorter than a distance from the image surface, oneplastic lens placed on the side of the deflecting means side has afunction of moving a beam position of a scanning direction to an opticalaxis at a portion close to a lens end portion, and the other lens placedon the side of the image surface has a function of further moving thebeam position of the scanning direction to the optical axis at a portionclose to the lens end portion.

Additional objects and advantages of the invention will be set forth inthe description which follows, and in part will be obvious from thedescription, or may be learned by practice of the invention. The objectand advantages of the invention may be realized and obtained by means ofthe instrumentalities and combinations particularly pointed out in theappended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of the specification, illustrate presently preferred embodiments ofthe invention, and together with the general description given above andthe detailed description of the preferred embodiments given below, serveto explain the principles of the invention.

FIG. 1 is a schematic cross-sectional view of an image forming device inwhich a multi-beam exposer unit is used according to an embodiment ofthe present invention;

FIG. 2 is a schematic plain view of a multi-beam exposer unit, which isincorporated into the image forming device of FIG. 1, according to anembodiment of the present invention;

FIG. 3 is a schematic cross-sectional view showing that a laser beamdeflected by an optical deflector is image-formed at a minimum distancein the optical scanning device of FIG. 2;

FIG. 4 is a graph explaining a state that a characteristic of an imageformation of the laser beam is improved by the multi-beam exposer unitof FIGS. 2 and 3, that is, a graph showing the relationship between amaximum beam diameter in the main scanning direction and the position ofthe main scanning direction and the relationship between a minimum beamdiameter in the main scanning direction and the position of the mainscanning direction when a position of the image surface is moved by ±2mm from a design value, in connection with laser beam LYa;

FIG. 5 is a graph explaining a state that a characteristic of an imageformation of the laser beam is improved by the multi-beam exposer unitof FIGS. 2 and 3, that is, a graph showing the relationship between amaximum beam diameter in the sub-scanning direction and the position ofthe main scanning direction and the relationship between a minimum beamdiameter in the sub-scanning direction and the position of the mainscanning direction when a position of the image surface is moved by ±2mm from a design value, in connection with laser beam LYa;

FIG. 6 is a graph explaining a state that a characteristic of an imageformation of the laser beam is improved by the multi-beam exposer unitof FIGS. 2 and 3, that is, a graph showing the relationship between amaximum amount of flare in the main scanning direction and the positionof the main scanning direction and the relationship between a maximumamount of flare in the sub-scanning direction and the position of themain scanning direction when a position of the image surface is moved by±2 mm from a design value, in connection with laser beam LYa;

FIG. 7 is a graph explaining a state that a characteristic of an imageformation of the laser beam is improved by the multi-beam exposer unitof FIGS. 2 and 3, that is, a graph showing the relationship between amaximum beam diameter in the main scanning direction and the position ofthe main scanning direction and the relationship between a minimum beamdiameter in the main scanning direction and the position of the mainscanning direction when a position of the image surface is moved by ±2mm from a design value, in connection with laser beam LMa;

FIG. 8 is a graph explaining a state that a characteristic of an imageformation of the laser beam is improved by the multi-beam exposer unitof FIGS. 2 and 3, that is, a graph showing the relationship between amaximum beam diameter in the sub-scanning direction and the position ofthe main scanning direction and the relationship between a minimum beamdiameter in the sub-scanning direction and the position of the mainscanning direction when a position of the image surface is moved by ±2mm from a design value, in connection with laser beam LMa;

FIG. 9 is a graph explaining a state that a characteristic of an imageformation of the laser beam is improved by the multi-beam exposer unitof FIGS. 2 and 3, that is, a graph showing the relationship between amaximum amount of flare in the main scanning direction and the positionof the main scanning direction and the relationship between a maximumamount of flare in the sub-scanning direction and the position of themain scanning direction when a position of the image surface is moved by±2 mm from a design value, in connection with laser beam LMa;

FIG. 10 is a graph explaining a state that a characteristic of an imageformation of the laser beam is improved by the multi-beam exposer unitof FIGS. 2 and 3, that is, a graph showing the relationship between amaximum beam diameter in the main scanning direction and the position ofthe main scanning direction and the relationship between a minimum beamdiameter in the main scanning direction and the position of the mainscanning direction when a position of the image surface is moved by ±2mm from a design value, in connection with laser beam LCa;

FIG. 11 is a graph explaining a state that a characteristic of an imageformation of the laser beam is improved by the multi-beam exposer unitof FIGS. 2 and 3, that is, a graph showing the relationship between amaximum beam diameter in the sub-scanning direction and the position ofthe main scanning direction and the relationship between a minimum beamdiameter in the sub-scanning direction and the position of the mainscanning direction when a position of the image surface is moved by ±2mm from a design value, in connection with laser beam LCa;

FIG. 12 is a graph explaining a state that a characteristic of an imageformation of the laser beam is improved by the multi-beam exposer unitof FIGS. 2 and 3, that is, a graph showing the relationship between amaximum amount of flare in the main scanning direction and the positionof the main scanning direction and the relationship between a maximumamount of flare in the sub-scanning direction and the position of themain scanning direction when a position of the image surface is moved by±2 mm from a design value, in connection with laser beam LCa;

FIG. 13 is a graph showing the relationship between an amount of defocus(amount of change in the position of image-formation) of the mainscanning direction and the position of the main scanning direction in astate that the image forming lens is detached in connection with thelaser beams LY in the multi-beam exposer unit of FIGS. 2 and 3 (LYa andLYb are arrayed with a predetermined distance in a predeterminedsub-scanning direction);

FIG. 14 is a graph showing the relationship between an amount of defocusof the sub-scanning direction and the position of the main scanningdirection in a state that the image forming lens is detached inconnection with the laser beams LY in the multi-beam exposer unit ofFIGS. 2 and 3;

FIG. 15 is a graph showing the relationship between an amount of a beamposition correction, which includes a difference between an actualposition of the image forming in the main scanning direction and alogical position of the image formation, and the position of the mainscanning direction in connection with the laser beams LY in themulti-beam exposer unit of FIGS. 2 and 3;

FIG. 16 is a graph showing the relationship between an amount of defocusof the main scanning direction and the position of the main scanningdirection in a state that the image forming lens is detached inconnection with the laser beams LM in the multi-beam exposer unit ofFIGS. 2 and 3;

FIG. 17 is a graph showing the relationship between an amount of defocusof the main scanning direction and the position of the sub-scanningdirection in a state that the image forming lens is detached inconnection with the laser beams LM in the multi-beam exposer unit ofFIGS. 2 and 3;

FIG. 18 is a graph showing the relationship between an amount of a beamposition correction, which includes a difference between an actualposition of the image forming in the main scanning direction and alogical position of the image formation, and the position of the mainscanning direction in connection with the laser beams LM in themulti-beam exposer unit of FIGS. 2 and 3;

FIG. 19 is a graph showing the relationship between an amount of defocusof the main scanning direction and the position of the main scanningdirection in a state that the image forming lens is detached inconnection with the laser beams LC in the multi-beam exposer unit ofFIGS. 2 and 3;

FIG. 20 is a graph showing the relationship between an amount of defocusof the sub-scanning direction and the position of the main scanningdirection in a state that the image forming lens is detached inconnection with the laser beams LC in the multi-beam exposer unit ofFIGS. 2 and 3;

FIG. 21 is a graph showing the relationship between an amount of a beamposition correction, which includes a difference between an actualposition of the image forming in the main scanning direction and alogical position of the image formation, and the position of the mainscanning direction in connection with the laser beams LC from themulti-beam exposer unit of FIGS. 2 and 3;

FIG. 22 is a schematic plain view showing a first modification of thepre-deflection optical system of the multi-beam exposer unit of FIGS. 2and 3;

FIGS. 23A and 23B are graphs each showing that the image-formingposition close to the main ray and the image-forming position close tothe outermost ray in a state that first and second finite focal lensesof the multi-beam exposer unit of FIG. 22 are estimated based on aspherical aberration of Table 3 so that the position of the imagesurface (surface of the photosensitive drum) is set to 0;

FIGS. 24A and 24B are graphs each showing a form of a wave-surfaceaberration and a corresponding amount of defocus when the sphericalaberration is optimized to minimize the maximum beam diameter within theamount of defocus of ±2.9 mm to the second degree;

FIGS. 25A and 25B are graphs each showing a form of a wave-surfaceaberration and a corresponding amount of defocus when the sphericalaberration is optimized to minimize the maximum beam diameter within theamount of defocus of ±2.9 mm to the fourth degree;

FIGS. 26A and 26B are graphs each showing a form of a wave-surfaceaberration and a corresponding amount of defocus when the sphericalaberration is optimized to minimize the maximum beam diameter within theamount of defocus of ±2.9 mm to the sixth degree;

FIGS. 27A and 27B are graphs each showing a form of a wave-surfaceaberration and a corresponding amount of defocus when the sphericalaberration is optimized to minimize the maximum beam diameter within theamount of defocus of ±2.9 mm to the eighth degree;

FIGS. 28A and 28B are graphs each showing a form of a wave-surfaceaberration and a corresponding amount of defocus when the sphericalaberration is optimized to minimize the maximum beam diameter within theamount of defocus of ±2.9 mm to the tenth degree;

FIGS. 29A and 29B are graphs each showing a form of a wave-surfaceaberration and a corresponding amount of defocus when the sphericalaberration is optimized to minimize the maximum beam diameter within theamount of defocus of ±2.9 mm to the twelfth degree;

FIGS. 30A and 30B are graphs each showing a form of a wave-surfaceaberration and a corresponding amount of defocus when the sphericalaberration is optimized to minimize the maximum beam diameter within theamount of defocus of ±2.9 mm spherical aberration of Table 3 to thefourteenth degree;

FIGS. 31A and 31B are graphs each showing a form of a wave-surfaceaberration and a corresponding amount of defocus when the sphericalaberration is optimized to minimize the maximum beam diameter within theamount of defocus of ±2.9 mm to the sixteenth degree;

FIG. 32 is a graph showing a maximum beam diameter in a predetermineddefocus at the time of each beam waist in a case where the first andsecond finite focal lenses of the multi-beam exposer unit of FIG. 22 arenot estimated based on the spherical aberration;

FIG. 33 is a schematic plain view showing an example in which the finitelens used in the multi-beam exposer unit of FIG. 22 is applied to themulti-beam exposer unit for a non-color;

FIG. 34 is a schematic cross-sectional view of the post-deflectionoptical system of the multi-beam exposer unit of FIG. 33;

FIG. 35 is a schematic cross-sectional view of the pre-deflectionoptical system of the multi-beam exposer unit of FIG. 33;

FIG. 36 is a schematic plain view showing a second modification of thepre-deflection optical system of the optical scanning device of FIGS. 2and 3;

FIG. 37 is a schematic plain view showing a third modification of thepre-deflection optical system of the optical scanning device of FIGS. 2and 3;

FIG. 38 is a schematic plain view showing a second modification of thepre-deflection optical system of the optical scanning device of FIGS. 2and 3;

FIG. 39 is a schematic plain view showing a second embodiment of thepre-deflection optical system of the optical scanning device of FIGS. 2and 3;

FIG. 40 is a graph showing the relationship between an amount of defocusof the main scanning direction and the position of the main scanningdirection in a state that the image-forming lens is detached inconnection with the laser beams LM in the multi-beam exposer unit inwhich the post-deflection optical system described by use of Tables 4and 5 is combined with the multi-beam exposer unit of FIGS. 2 and 3;

FIG. 41 is a graph showing the relationship between an amount of defocusof the sub-scanning direction and the position of the main scanningdirection in a state that the image-forming lens is detached inconnection with the laser beams LM in the multi-beam exposer unit inwhich the post-deflection optical system described by use of Tables 4and 5 is combined with the multi-beam exposer unit of FIGS. 2 and 3;

FIG. 42 is a graph showing the relationship between an amount of a beamposition correction, which includes a difference between an actualposition of the image forming in the main scanning direction and alogical position of the image formation, and the position of the mainscanning direction in connection with the laser beams LM in which thepost-deflection optical system described by use of Tables 4 and 5 iscombined with the multi-beam exposer unit of FIGS. 2 and 3;

FIG. 43 is a schematic plain view showing a second modification of theoptical scanning device of FIG. 39;

FIG. 44 is a graph showing the relationship between an amount of defocusof the main scanning direction and the position of the main scanningdirection in a state that the image-forming lens is detached inconnection with the laser beam LM in the multi-beam exposer unit inwhich the post-deflection optical system described by use of Tables 6and 7 is combined with the multi-beam exposer unit of FIGS. 2 and 3;

FIG. 45 is a graph showing the relationship between an amount of defocusof the sub-scanning direction and the position of the main scanningdirection in a state that the image-forming lens is detached inconnection with the laser beam LM in the multi-beam exposer unit inwhich the post-deflection optical system described by use of Tables 6and 7 is combined with the multi-beam exposer unit of FIGS. 2 and 3; and

FIG. 46 is a graph showing the relationship between an amount of a beamposition correction, which includes a difference between an actualposition of the image forming in the main scanning direction and alogical position of the image formation, and the position of the mainscanning direction in connection with the laser beam LM in which thepost-deflection optical system described by use of Tables 6 and 7 iscombined with the multi-beam exposer unit of FIGS. 2 and 3.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Embodiments of the present invention will be described with reference tothe drawings.

FIG. 1 shows a color image forming apparatus in which a multi-beamexposer unit of the embodiment of the present invention is used. In thiskind of color image forming apparatus four kinds of image data are used,which are color-separated into color components, Y (Yellow), M(Magenta), C (Cyan), and B (Black), and four sets of various devices forforming an image corresponding to each of the color components. In thefollowing explanation, marks Y, M, C, and B are added to the respectivereference numerals to differentiate between the image data of each colorcomponent and the corresponding device.

As shown in FIG. 1, an image forming device 100 has first to fourthimage forming units 50Y, 50M, 50C, and 50B for forming an image of eachof components, which are color-separated into Y (Yellow), M (Magenta), C(Cyan), and B (Black).

The respective image forming units 50 (Y, M, C, B) are provided under alaser exposer unit 1 in series in order of 50Y, 50M, 50C, and 50B so asto correspond to the position where the laser beams LY, LM, LC, and LBcorresponding to the respective color components are emitted through therespective mirrors 37B, 37Y, 37M, and 37C.

A transfer belt 52 is stretched onto a belt drive roller 56, which isrotated in a direction of an arrow, and a tension roller 54. Thetransfer belt 52 is rotated in a direction where the belt drive roller56 is driven at a predetermined speed.

The respective image forming units 50Y, 50M, 50C, and 50B includephotosensitive drums 58Y, 58M, 58C, and 58B.

Each of the photosensitive drums is cylindrically shaped to be rotatablein a direction of an arrow, and forms an electrostatic latent imagecorresponding to the image exposed by the exposer unit 1.

There are arranged charge units 60 (Y, M, C, B), developing units 62 (Y,M, C, B), transfer units 64 (Y, M, C, B), cleaner 66 (Y, M, C, B), anddischarge units 68 (Y, M, C, B) around the photosensitive drums 58 (Y,M, C, B) in order along the direction where, the photosensitive drums 58(Y, M, C, B) are rotated.

Each of the charge units 60 provides a predetermined voltage onto thesurface of each of the respective photosensitive drums 58 (Y, M, C, B).

Each of the developing units 62 develops the characteristic latent imageon the surface of each of the photosensitive drums 58 (Y, M, C, B) withtoner to which the corresponding color is provided.

Each of the transfer units 64 transfers a toner image, which is formedon each of the photosensitive drums 58, to a recording medium, which istransferred through the transfer belt 52, in a state that the transferbelt 52 is provided between each photosensitive drum 58 and eachtransfer unit 64 so that it is opposite to each photosensitive drum 58.

Each of the cleaners 66 removes the residual toner, which is left oneach of the photosensitive drums 58 after each toner image istransferred through each of the transfer units 64.

Each of the discharge units 68 removes the residual voltage, which isleft on each of the photosensitive drums after each toner image istransferred through each of the transfer units 64.

Irradiation of the laser beams LY, LM, LC, and LB, which arerespectively guided to the photosensitive drums 58 through therespective mirrors 37Y, 37M, 37C, and 33B, is provided between each ofthe charge units 60 (Y, M, C, B) and each of the developing units 62 (Y,M, C, B).

A paper cassette 70 is provided under the transfer belt 62 to containthe recording medium for transferring the image formed by each of theimage forming units 50 (Y, M, C, B), that is, paper P.

A feeding roller 72 having a semicircular cross section is provided atthe position, which is one end portion of the paper cassette 70 and aportion close to the tension roller 54, so as to pick up paper Pcontained in the paper cassette 70 one by one from the uppermostsection.

A resist roller 74 is provided between the feeding roller 72 and thetension roller 54. The resist roller 74 is used to conform to the topend of one paper P, which is picked up from the cassette 70, to the topend of each toner image formed on the respective image forming units 50,particularly the toner image formed on the photosensitive drum 58 by theimage forming unit 50B.

An absorption roller 76 is provided at a portion between the resistroller 74 and the first image forming unit 50Y, that is, a portion closeto the tension roller 54, substantially on an outer periphery of thetension roller 54. The absorption roller 76 provides a predeterminedelectrostatic absorption onto one paper P transferred at a predeterminedtiming by the resist roller 72.

Resist sensors 78 and 80 are provided at a portion, which is an endportion of the transfer belt 52, and close to the belt drive roller 56,substantially on an outer periphery of the belt drive roller 56 to havea predetermined distance in an axial direction of the belt drive roller56. The resist sensors 78 and 80 detect the position of the image formedon the transfer belt 52 (FIG. 1 is the front cross-sectional viewshowing only the back sensor 80).

A transfer belt cleaner 82 is provided on the transfer belt 52corresponding to the outer periphery of the belt drive roller 56. Thetransfer belt cleaner 82 removes toner adhered onto the transfer belt 52or paper dust from paper P.

A fixing unit 84 is provided in a direction where paper P transferredthrough the transfer belt 52 is detached from the belt drive roller 56and further transferred. The fixing unit 84 is used to fix the tonerimage, which is transferred onto paper P, to paper P.

FIGS. 2 and 3 show the multi-beam exposer unit, which is used in theimage forming apparatus of FIG. 1. In the color image forming apparatusof FIG. 1, four kinds of image data are used, which are color-separatedinto color components, Y (Yellow), M (Magenta), C (Cyan), and B (Black),and four sets of various devices for forming an image corresponding toeach of the color components. In the following explanation, marks Y, M,C, and B are added to the respective reference numerals to makediscrimination between image data of each color component and thecorresponding device.

As shown in FIGS. 2 and 3, the multi-beam exposer apparatus 1 has onlyone polygon mirror unit 5 as deflecting means for deflecting the laserbeams. The polygon mirror unit 5 deflects each of the laser beamsemitted from each of the laser elements, serving as a light source, to apredetermined position of each of the image surfaces, that is, each ofthe photosensitive drums 58 (Y, M, C, B) of the first to fourth imageforming sections 50 (Y, M, C, B) at a predetermined linear speed. Inthis case, a direction where the laser beam is deflected by each of thereflection surfaces of the polygon mirror unit 5 is hereinafter calledthe main scanning direction. Moreover, a direction, which isperpendicular to the main scanning direction and which is parallel toeach reflection surface of a polygon mirror body 5 a, is called thesub-scanning direction.

The polygon mirror body 5 a may be formed of, for example, aluminum.Each of the reflection surfaces of the polygon mirror body 5 a is cutalong the surface including a direction where the polygon mirror body 5a is rotated, that is, the surface perpendicular to the main scanningdirection. In other words, after the surface is cut along thesub-scanning direction, and a surface protection layer such as siliconoxide (SiO₂) is deposited on the cut surface.

A post-deflection optical system 21 is provided between the polygonmirror unit 5 and the image surface in order to provide a predeterminedoptical characteristic to each of the laser beams L (Y, M, C, B)deflected to a predetermined direction by each of the reflected surfacesof the polygon mirror unit 5.

In order to adjust the horizontal synchronization of the respectivelaser beams L (Y, M, C, and B) deflected by the polygon mirror unit 5,the post-deflection optical system 21 comprises a horizontalsynchronization detector 23, a mirror 25 for horizontal synchronization,an image forming lens 30 including first and second image forming lenses30 a and 30 b, a plurality of mirrors 33Y (first yellow), 35Y (secondyellow), 37Y (third yellow), 33M (first magenta), 35M (second magenta),37M (third magenta), 33C (first cyan), 35C (second cyan), 37C (thirdcyan), and 33B (for black), and dust prevention glasses 39 (Y, M, C, M).

The horizontal synchronization detector 23 detects each laser beam L.The mirror 25 is used to reflect each laser beam L toward the detector23. The image forming lens 30 is used to optimize the shape and positionof a beam spot on the image surface (photosensitive drum 58 of FIG. 1)of each laser beams L (Y, M, C, M) deflected by each reflection surfaceof the polygon mirror body 5 a. The plurality of the mirrors are used toguide each laser beam L (Y, M, C, and B) emitted from the second imageforming lens 30 b to each photosensitive drum 58 (Y, M, C, B)corresponding to each laser beam. The dust prevention glasses 39 areused to prevent the laser exposer unit 1 from being accumulated.

The following will explain the pre-deflection optical system between thelight source (laser element) and the polygon mirror unit as a firstembodiment of the present invention.

The laser exposer unit 1 has first to fourth light sources 3Y, 3M, 3C,and 3B (M, M=positive integral number, 4 in this case) including firstand second (NI=N1=N2=N3=N4=2) (for yellow, magenta, cyan, and black)laser elements satisfying Ni≧2. Then, the first to fourth light sourcesgenerate the laser beam corresponding to image data, which iscolor-separated into color components.

The first to fourth light sources 3Y, 3M, 3C, and 3B include first andsecond yellow lasers 3Ya and 3Yb for emitting laser beams correspondingto yellow images, first and second magenta lasers 3Ma and 3Mb foremitting laser beams corresponding to magenta images, first and secondcyan lasers 3Ca and 3Cb for emitting laser beams corresponding to cyanimages, and first and second black lasers 3Ma and 3Mb for emitting laserbeams corresponding to black images. In this case, first to fourth laserbeams, that is, paired LYa and LYb, paired LMa and LMb, paired LCa andLCb, and paired LBa and LBb are emitted from each of the laser elements.

Four pairs of pre-deflection optical systems 7 (Y, M, C, B) are arrangedbetween the respective laser beam elements 3Ya, 3Ma, 3Ca, 3Ba and thepolygon mirror unit 5 a. The respective pre-deflection optical systems 7are used to provide a predetermined shape of a cross section beam spotof each of the laser beams LYa, LMa, LCa, and LBa emitted from each ofthe light sources 3Ya, 3Ma, 3Ca, and 3Ba.

The following will explain the characteristics of half mirrors 11B andcylinder lens 12B of the pre-deflection optical system 7 in which thelaser beam LBa guided to the polygon mirror unit 5 from the first blacklaser 3Ba and the laser beam LBb guided to the polygon mirror unit 5from the second black laser 3Bb are shown as a typical example.

A predetermined convergence is provided to the dispersive laser beam LBaemitted from the first black laser 3Ba by a finite focus lens 8Ba. Thelaser beam LBa is reflected to the half mirror 11B by mirror 9Ba. Thelaser beam LBa reflected by the mirror 9Ba is passed through the halfmirror 11B to be made incident onto the cylinder lens 12B. The laserbeam LBa, which is made incident on the cylinder lens 12B, is furtherconverged in only the sub-scanning direction by the lens 12 so as to beguided to the polygon mirror unit 5.

Similarly, a predetermined convergence is provided to the dispersivelaser beam LBb emitted from the second black laser 3Bb by a finite focuslens 8Bb. The laser beam LBb is reflected to the half mirror 11B bymirror 9Bb. The laser beam LBb reflected by the mirror 9Bb is madeincident onto the surface, which is opposite to the surface where thelaser beam LBa is made incident from the first black laser 3Ba, to havea predetermined beam distance between the laser beams LBa and LBb in thesub-scanning direction. The laser beam LBb is further reflected by thehalf mirror 11B to be made incident onto the cylinder lens 12B.

The laser beam LBb, which is made incident on the cylinder lens 12B, isfurther converged in only the sub-scanning direction by the lens 12B soas to be guided to the polygon mirror unit 5.

The finite focus lenses 8Ba and 8Bb use a single lens, which is formedby adhering a plastic aspherical lens (not shown) onto aspherical glasslens, or a single aspherical glass lens. As a plastic aspherical glasslens, a UV curing plastic aspherical lens, which is cured by irradiationof an ultraviolet ray, is preferably used. Also, substantially the samecharacteristic is provided to each of the finite focus lenses 8Ba and8Bb.

As mirrors 9Ba and 9Bb, there is a motor drive mirror (galvano mirror),which is formed such that the angle of the reflection surface (notshown) can be changed to an arbitrary angle by a galvano motor or avoice coil in a state such that each of the main scanning andsub-scanning directions is used as a rotation axis. The half mirror 11Bis formed to have a thickness tm of 5 mm by depositing the metal film onone surface of the parallel plane glasses having the same thickness andmaterial so that a ratio between transmittance and reflectance iscontrolled to a predetermined value.

The cylinder lens 12B is a hybrid lens, which is obtained by bonding aplastic cylinder lens formed of PMMA and a glass cylinder lens formed ofFD 60 to each other or pressing these lenses to a positioning member(not shown) from a predetermined direction to be integral with eachother. In this case, curvature of the surface where the plastic cylinderlens and the glass cylinder lens contact each other in the sub-scanningdirection is equally set. Moreover, the plastic cylinder lens is moldedto be integral with the glass cylinder lens. In the plastic cylinderlens, the cross section in the sub-scanning direction is formed on apart of the cylindrical surface such that the surface contacting air haspower in the sub-scanning direction.

The positions of the laser beams LBa and LBb passing through thecylinder lens 12B are out of the optical axis of the cylinder lens 12B.In other words, the laser beams LBa and LBb are decentered and inclinedin the sub-scanning direction to be incident on the cylinder lens 12B.That is, the laser beams LBa and LBb directing to the polygon mirrorunit 5 from the half mirror 11B are arranged so as to cancel the comaaberration, which is generated when the laser beams LBa and LBb passthrough the first and second image forming lenses 30 a and 30 b. Also,the laser beam LBb is incident to be asymmetrical to the laser beam LBawith respect to the optical axis of the cylinder lens.

The respective laser beams LBa and LBb are combined as substantially onelaser beam having a predetermined beam distance in the sub-scanningdirection through the half mirror 11B. The laser beams LBa and LBb arepassed through a non-reflection area of a laser synchronization mirror13, that is, a predetermined position of the mirror 13 having no mirrorportion formed to be guided to the polygon mirror unit 5.

The laser beams LBa and LBb guided to the polygon mirror unit 5 aresubstantially linearly focused nearby each reflection surface of thepolygon mirror body 5 a. Then, the laser beams LBa and LBb are madeincident on the incident surface of the first image forming lens 30 aincluded in the image forming lens 30 of the post-deflection opticalsystem 21 at a predetermined angle.

Thereafter, predetermined convergence and directivity are given to thelaser beams LBa and LBb by the second image forming lens 30 b to havepredetermined shape and size of the beam spot on the surface of thephotosensitive drum 58B. The laser beams LBa and LBb are reflected at apredetermined angle by the mirror 33B, and passed through the dustprevention glass 39B. Then, the photosensitive drum 58 is irradiatedwith the laser beams LBa and LBb.

Next, the following will explain the characteristic of the half mirrors11 (Y, M, C, and B).

The laser beams LYa, LMa, LCa, and LBa emitted from the laser elements3Ya, 3Ma, 3Ca and 3Ba are transmitted through the half mirrors 11 (Y, M,C, and B), respectively. The laser beams LYb, LMb, LCb, and LBb emittedfrom the laser elements 3Yb, 3Mb, 3Cb and 3Bb are reflected by the halfmirrors 11 (Y, M, C, B), respectively. Since the number of therespective light sources 3 (Y, M, C, B) is Ni (Ni=positive integralnumber, in this case, N1=N2=N3=N4=2), it is needless to say that(Ni−1)=1 half mirrors 11 (Y, M, C, and B) is used for each light source.

The number of times of the transmission of the laser beams L (Ya, Yb,Ma, Mb, Ca, Cb, Ba, Bb) through the half mirrors 11 (Y, M, C, B) is 1 or0, respectively. More specifically, LBa, LMa, LCa, and LYa are passedthrough the half mirrors 11 (Y, M, C, and B) only one time. The otherlaser beams LBb, LMb, LCb, and LYb are reflected by the half mirrors 11(Y, M, C, B), respectively. The respective half mirrors 11 (Y, M, C, B)are inclined in the same direction and at the same angle with respect tothe laser beams LBa, LMa, LCa, and LYa directing to the polygon mirrorunit 5 through the respective half mirrors 11 (Y, M, C, B). In thiscase, an angle of each of half mirrors 11 (Y, M, C, B) to be inclined is45°. Also, a thickness tm of each of the half mirrors 11 (Y, M, C, B) isset to 5 mm.

If the ratio between transmittance and reflectance of the respectivehalf mirrors 11 (Y, M, C, B) is set to 1:1, the outputs of the laserelements 3Ya and 3Yb, 3Ma and 3Mb, 3Ca and 3Cb, and 3Ba and 3Bb of therespective light sources 3 (Y, M, C, B) can be set to substantially thesame power. Thereby, the outputs on the image forming surface can be setto the same, and the image forming characteristics of the laser beams L(Ya, Yb, Ma, Mb, Ca, Cb, Ba and Bb) can be easily equalized.

There is provided a holding member 15, which is formed to be integralwith a unit housing as a fixing member, and a cover plate 15 a forcovering the holding member 15 to seal the polygon mirror body 5 aaround the polygon mirror unit 5.

In a predetermined area of the holding member 15, which is positioned inthe vicinity of the line connecting the polygon mirror unit 5 and thelaser synchronization mirror 13, a dust prevention glass 14 is provided.The dust prevention glass 14 is used together with the holding member15. Thereby, the polygon mirror body 5 a is sealed, and the respectivelaser beams L (Ya, Yb, Ma, Mb, Ca, Cb, Ba, and Bb) are transmitted tothe respective reflection surfaces of the polygon mirror body 5 a.

In a predetermined area of the holding member 15, which is positioned ina direction where the laser beams L (Ya, Yb, Ma, Mb, Ca, Cb, Ba, Bb)deflected by the respective reflection surfaces of the polygon mirrorbody 5 a are emitted, a cover 16 is provided. The cover 16 is formed ofthe material having the same optical characteristic as the dustprevention glass 14. The cover 16 is used together with the holdingmember 15. Thereby, the polygon mirror body 5 a is sealed, and therespective laser beams L (La, Yb, Ma, Mb, Ca, Cb, Ba, Bb), which aredeflected on the respective reflection surfaces, are passed through thecover 16.

The holding member 15, the cover plate 15 a, the dust prevention glass14, and the cover 16 reduce noise, which is generated when the polygonmirror body 5 a is rotated at high speed, wind loss of the respectivereflection surfaces of the polygon mirror body 5 a, and dust adhesiononto a bearing of the holding portion of the polygon mirror body 5 a.

As the dust prevention glass 14, a parallel plate, which is formed ofthe same material as each half mirror 11 (Y, M, C, B) (BK 7 in thiscase), is used. In the example of FIG. 2, the thickness tg of the dustprevention glass 14 is set to 5 mm. Then, the dust prevention glass 14is placed in a direction, which is opposite to each half mirror 11 (Y,M, C, B) to sandwich the optical axis with respect to the directionwhere the respective half mirrors 11 (Y, M, C, B) are inclined, that is,22.5°. In a case where the direction of the inclination of each halfmirror 11 is positive (+), the dust prevention glass 14 is inclined at−22.5°. If the dust prevention glass 14 is inclined at −45°, it ispossible to cancel the aberration component, which is given to each ofthe laser beams LBa, LMa, LCa, LYa transmitted through each of the halfmirrors 11 (Y, M, C, B) by each of the half mirrors 11 (Y, M, C, B).However, a new aberration component will be given to the laser beamsLBb, LMb, LCb, and LYb reflected by the respective half mirrors 11 (Y,M, C, B). Therefore, an inclination angle ug at which the dustprevention glass 14 is inclined is set to −22.5° such that theaberration components to be given to the laser beams LBa, LMa, LCa, andLYa by the respective half mirrors 11 (Y, M, C, B) and the aberrationcomponents to be given to the laser beams LBb, LMb, LCb, and LYb by thedust prevention glass 14 can be set to minimum values (mark “−” showsthe direction, which is opposite to the direction of the inclination ofthe half mirror). The dust prevention glass 14 may be slightly inclinedin the sub-scanning direction to prevent stray light (not shown), whichis generated by the reflection of the respective laser beams due to thefirst and second image forming lenses 30 a and 30 b, from being returnedto the polygon mirror unit 5. Or, there may be used a wedge plate whoseincident and emission surfaces have inclinations in the sub-scanningdirection.

In the multi-beam exposer unit of FIGS. 2 and 3, the laser beams LBa,LMa, LCa, and LYa, which transmit through the half mirrors 11 (Y, M, C,B), respectively, are obliquely incident on the incident surfaces of thehalf mirrors 11 (Y, M, C, B). Due to this, spherical aberration B, comaaberration F, astigmatism C, and variation of focal length Δf aregenerated. If the relationship between the inclination of the halfmirror 11 and that of the dust prevention glass 14 is evaluated,spherical aberration ΣBi, comma aberration ΣFi, astigmatism ΣCi, andvariations of focal length Δf can be shown by the following equations(1) to (4):

 ΣBi=−ti×ui ⁴×(ni ²−1)/ni ³  (1)

ΣFi=−ti×ui ³×(ni ²−1)/ni ³  (2)

ΣCi=−ti×ui ²×(ni ²−1)/ni ³  (3)

Δf=Σ(ti ×(1−1/ni))  (4)

wherein the order of the arrangement of the half mirrors and the dustprevention glass is i, the thickness of the half mirror is t,reflectance is n, and the incident angle is u.

The variation of the focal length Δf can be completely canceled byincreasing the length of the optical path by Σ(ti×(1−1/ni)). In thiscase, the length of the optical path is the distance between the finitelenses (8Ya, 8Ma, 8Ca, 8Ba) and the corresponding cylinder lenses 11 (Y,M, C, B).

The comma aberration ΣFi can be canceled by setting the mark, ui,reversely, that is, ui″*−ui, as is obvious from equation (2). Therefore,the components, which generate the coma aberration having the reversemark, are arranged such that the absolute value of the sum of theaberrations generated by the half mirrors 11 and the dust preventionglass 14 becomes minimum. In other words, if the angle, which is formedby the dust prevention glass 39 and the incident laser beam, is 45°, thedust prevention glass 39 is inclined in the opposite direction withrespect to the angle, which is formed by the half mirrors 11 and thelaser beam passing through the half mirror 11. Thereby, the absolutevalue of the entire coma aberration can be reduced. It is assumed that acoma aberration, which is generated when a certain beam passes throughthe i-th half mirror, is Fi. Then, if the beam passes through a (i=1 toa) half mirrors in all, a thickness tg of a correction plate g(corresponding to the dust prevention glass 14 in this applicationthough the parallel plane plate is generally used) to be inserted to theoptical path to cancel the coma aberration and an inclination angle ugcan be set based on the following equation (5):

 −tg×ug ³×(ng ²−1)/ng ³=−(F 1+F 2+ . . . +Fa)  (5)

In order to make the number of the correction plates (the parallel planeplates) minimum, there can be considered a method in which the absolutevalues of the coma aberration of the laser beam whose coma aberration ismaximum and the laser beam whose coma aberration is minimum are set tobe the same.

For example, it is assumed that the laser beam whose coma aberration ismaximum is shown by (F1+F2+ . . . +Fa) as shown in equation (5) and thecoma aberration of the laser beam whose coma aberration is minus is 0(there exists the laser beam, which does not transmit through theparallel plate).

The thickness tg of the correction plate g is set to satisfy thefollowing equation (6), and the correction plate g is placed such thatthe angle, which is formed by the incident laser beam and the correctionplate g, becomes ug:

−tg×ug ³×(ng ²−1)/ng ³=−(F 1+F 2+ . . . +Fa)/2  (6)

As a result, the maximum absolute value of the coma aberration can beset to (F1+F2+ . . . Fa)/2, that is, the half of the case in which nocorrection plate g exists.

In the multi-beam exposer unit of FIGS. 2 and 3, only the half mirrorsare used. It is assumed that the coma aberration generated by the halfmirror 11 is F1.

The correction plate (parallel plane plate) having the thickness tgsatisfying the following equation (7) is placed such that the angle ug,which is formed by the incident laser beam and the correction plate g,becomes ug.

−tg×ug ³×(ng ²−1)/ng ³ =−F 1/2  (7)

As a result, the maximum absolute value of the coma aberration can be ½of F1. This conforms to the inclination angle of the dust preventionglass 14.

Next, the following will specifically explain the advantage, which isbrought about by the dust prevention glass 14.

FIGS. 4 to 6, FIGS. 7 to 9, and FIGS. 10 to 12 are graphs each showingthe characteristic of the laser beam guided from the multi-beam exposerunit to the corresponding photosensitive drum.

FIG. 4 is a graph explaining a state that a characteristic of an imageformation of the laser beam is improved by the multi-beam exposer unitof FIGS. 2 and 3, that is, a graph showing the relationship between amaximum beam diameter in the main scanning direction and the position ofthe main scanning direction and the relationship between a minimum beamdiameter in the main scanning direction and the position of the mainscanning direction when a position of the image surface is moved by ±2mm from a design value, in connection with laser beam LYa. FIG. 5 is agraph explaining a state that a characteristic of an image formation ofthe laser beam is improved by the multi-beam exposer unit of FIGS. 2 and3, that is, a graph showing the relationship between a maximum beamdiameter in the sub-scanning direction and the position of the mainscanning direction and the relationship between a minimum beam diameterin the sub-scanning direction and the position of the main scanningdirection when a position of the image surface is moved by ±2 mm from adesign value, in connection with laser beam LYa. FIG. 6 is a graphexplaining a state that a characteristic of an image formation of thelaser beam is improved by the multi-beam exposer unit of FIGS. 2 and 3,that is, a graph showing the relationship between a maximum amount offlare in the main scanning direction and the position of the mainscanning direction and the relationship between a maximum amount offlare in the sub-scanning direction and the position of the mainscanning direction when a position of the image surface is moved by ±2mm from a design value, in connection with laser beam LYa.

In FIGS. 4 to 6, curves DYMAXa and DYMAXp show the change of the maximumbeam diameter of the main scanning direction, curves DYMINa and DYMINpshow the change of the minimum beam diameter of the main scanningdirection. Curves DZMAXa and DZMAXp show the change of the maximum beamdiameter of the sub-scanning direction, curves DZMINa and DZMINp showthe change of the minimum beam diameter of the sub-scanning direction.Curves FLRYMAXa and FLRYMAXp show the change of the maximum amount offlare of the main scanning direction, and curves FLRZMAXa and FLRZMAXpshow the change of the maximum amount of flare of the sub-scanningdirection. A subscript p, which is added to the display of each curveshows the characteristic of the case in which the dust prevention glass(correction plate) 14 of the multi-beam exposer unit is provided. Asubscript a shows the state in which the dust prevention glass 14 isintentionally detached for comparison. Subscripts f, g, and h show thatthe characteristics provided by the modification to be described laterare displayed on the same scale.

FIGS. 7 to 9 show the characteristic of the laser beam LMa from thefirst magenta laser 3Ma under the same condition as FIGS. 4 to 6. Sincethe marks of the curves of these figures are the same as the cases ofFIGS. 4 to 6, the specific explanation is omitted.

FIGS. 10 to 12 show the characteristic of the laser beam LCa from thefirst cyan laser 3Ma under the same condition as FIGS. 4 to 6. Since themarks of the curves of these figures are the same as the cases of FIGS.4 to 6, the specific explanation is omitted.

Since the laser beam LBa emitted from the first black laser 3Ba hassubstantially the same characteristic as the laser beam LYa from thefirst yellow laser 3Ya, the specific explanation of the laser beam LBais omitted.

As explained above, in the pre-deflection optical system 7, the comaaberration components, which are generated in only the laser beams LYa,LMa, LCa, and LBa passing through the half mirrors 11 (Y, M, C, B) areset so as to have the minimum difference of the absolute value betweenthe above coma aberration and the coma aberration among the laser beamsLYb, LMb, LCb, LBb reflected without passing through the half mirrors 11(Y, M, C, B) by the dust prevention glass 14 (parallel plane plate). Thedust prevention glass 14 is placed at the angle which corresponds to ½angle and each half mirror 11 is inclined in the direction opposite tothe direction where each half mirror 11 is inclined with respect to theoptical axis. Thereby, the variation of the beam diameter of the mainscanning direction and that of the beam diameter of the sub-scanningdirection can be reduced. It is recognized that the amount of flare canbe improved in both the main and sub-scanning directions.

The following will specifically explain the post-deflection opticalsystem between the polygon mirror unit and the image surface accordingto the second embodiment of the present invention.

As shown in FIGS. 2 and 3, the post-deflection optical system 21 has oneset of image forming lenses 30 including first and second image forminglenses 30 a and 30 b. By use of Tables 1 and 2, and equation (8), thefollowing optical characteristic and shape are given. Each of the imageforming lenses 30 a and 30 b is placed at a predetermined position,which is defined such that the distance from the reflection point ofeach reflection surface of the polygon mirror becomes shorter than thedistance from the image surface. $\begin{matrix}{X = {\frac{{CUY}_{y}^{2} + {CUZ}_{z}^{2}}{1 + \sqrt{1 - {CUY}_{y}^{2} - {CUZ}_{z}^{2}}} + {\sum\limits_{n = 0}^{4}{\sum\limits_{m = 0}^{10}{{AmnY}^{m}Z^{zn}}}}}} & (8)\end{matrix}$

TABLE 1 absolute coordinates: Decentering Post-deflection optical systemin y direction −4.333 curvature lens surface CUY CUZ Thickness numbermaterial 0.019021 −0.0147546 −35.435 1 air 0.02040817 0.01793626 −6.5242 PMMA 0.0029042340 −0.00634328 −106.530 3 air 0.002112237 0.01552636−6.0077405 4 PMMA plane plane −9.0000 air plane plane −2.000 BK7 planeplane −164.000 air

TABLE 2 Lens surface number:1 n\m 0 1 2 3 4 5 0 0.000E+00 −5.175E−020.000E+00 3.402E−05 −5.413E−06 −8.876E−09 1 0.000E+00 −5.988E−061.407E−07 1.467E−07 1.155E−08 −6.891E−10 2 −8.696E−05 −3.944E−06−4.335E−07 5.183E−08 −1.916E−09 4.486E−11 3 1.008E−05 7.221E−082.189E−08 −1.459E−09 1.338E−10 −8.773E−12 4 −2.309E−07 −1.553E−10−5.827E−10 4.448E−11 −9.423E−13 0.000E+00 n\m 6 7 8 9 10 0 −3.297E−103.380E−11 −6.406E−13 −1.116E−14 7.120E−16 1 6.566E−12 −5.297E−131.169E−14 5.802E−16 −1.260E−17 2 3.950E−12 −2.012E−13 −4.174E−17−3.424E−16 1.399E−17 3 −1.468E−13 1.466E−14 −1.448E−16 2.661E−17−9.120E−19 4 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 Lenssurface number:2 n\m 0 1 2 3 4 5 0 0.000E+00 −6.667E−02 0.000E+002.044E−05 −4.684E−06 7.391E−09 1 0.000E+00 −1.127E−06 −2.689E−061.774E−07 −1.558E−09 −2.888E−10 2 2.387E−05 −4.140E−06 −3.284E−073.799E−08 2.264E−12 6.067E−12 3 −8.930E−06 1.961E−07 1.661E−08−2.529E−09 6.180E−11 2.810E−12 4 2.522E−07 −3.095E−09 −5.120E−104.207E−11 −9.508E−13 0.000E+00 n\m 6 7 8 9 10 0 −9.888E−10 1.234E−11−2.037E−13 −9.521E−17 2.607E−16 1 2.046E−11 −7.927E−13 5.657E−15−3.536E−16 1.618E−17 2 −2.478E−12 −6.435E−14 3.196E−15 1.237E−16−3.821E−18 3 −2.949E−14 −6.090E−15 6.149E−17 4.649E−18 −6.623E−20 40.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 Lens surface number:3n\m 0 1 2 3 4 5 0 0.000E+00 1.660E−02 0.000E+00 −3.927E−06 −2.133E−073.818E−10 1 0.000E+00 −2.644E−05 5.823E−07 −1.140E−10 8.057E−111.705E−13 2 −8.028E−06 −5.092E−08 1.020E−11 1.569E−11 −6.288E−15−2.339E−16 3 −3.363E−09 1.290E−10 3.133E−12 5.319E−14 −8.741E−17−2.001E−18 4 2.025E−10 1.118E−12 −8.987E−15 −1.688E−16 −9.048E−180.000E+00 n\m 6 7 8 9 10 0 1.505E−11 2.572E−14 −8.037E−16 1.475E−18−1.904E−20 1 −1.613E−14 7.102E−17 −8.131E−19 3.084E−21 1.349E−23 21.893E−17 −6.265E−19 1.203E−21 3.247E−23 −1.577E−25 3 1.135E−19−3.473E−22 6.745E−24 −4.288E−27 −5.142E−29 4 0.000E+00 0.000E+000.000E+00 0.000E+00 0.000E+00 Lens surface number:4 n\m 0 1 2 3 4 5 00.000E+00 1.022E−02 0.000E+00 −4.091E−06 −4.387E−08 4.082E−10 10.000E+00 −1.972E−05 3.253E−07 −1.081E−09 2.945E−11 2.841E−13 2−8.691E−06 −5.126E−08 2.922E−10 1.530E−11 −1.618E−15 −1.539E−15 3−8.160E−09 4.185E−11 1.989E−12 4.893E−14 2.992E−16 2.713E−18 4 1.656E−101.372E−12 −3.279E−15 −1.813E−16 −7.667E−18 0.000E+00 n\m 6 7 8 9 10 01.591E−12 9.148E−16 2.739E−16 4.265E−18 −7.011E−20 1 −9.708E−161.800E−17 −1.643E−18 1.058E−20 −3.151E−23 2 −3.743E−18 −6.221E−202.589E−21 −1.455E−23 −9.009E−26 3 7.095E−20 −6.659E−22 −5.008E−24−4.140E−26 1.614E−27 4 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

The shapes shown in Tables 1 and 2 and equation (8) are given to thefirst and second image forming lenses 30 a and 30 b, so that thepositional shift of the beam on the image surface in the sub-scanningdirection caused by the tilt of the reflection surface of the polygonmirror can be controlled to 3 μm. In other words, the post-deflectionoptical system has a function of correcting the positional shift of thebeam, which is generated by influence caused by the difference betweeninclinations of the respective reflection surfaces of the polygonmirror. Thereby, the shape, which satisfies the interpolationrelationship in the sub-scanning direction, is given to the first andsecond image forming lenses 30 a and 30 b over the entire scanning area.As a result, as compared with the case having no function of correctingthe positional shift, that is, 192 μm, the positional shift of the beamon the image surface in the sub-scanning direction can be controlled to3 μm, a correction magnification is {fraction (1/64)} (in the case inwhich the inclination of each reflection mirror of the polygon mirrorbody 5 a is one minute ({fraction (1/60)} degree)). In the case wherethe post-deflection optical system has no function of correcting thepositional shift, the upper limit of an allowable value of inclinationof each reflection mirror of the polygon mirror body 5 a is about onesecond ({fraction (1/3600)} degree). In this case, to satisfy theallowable value of the inclination by only the accuracy of working thepolygonal mirror body 5 a, the working is extremely complicated, so thatthe yield becomes worse. Even if the allowable value is satisfied, themanufacturing cost is greatly increased.

FIGS. 13 to 15, and FIGS. 16 to 18, and FIGS. 19 to 21 show graphs eachshowing the optical function of each of the image forming lenses 30 aand 30 b to explain the state that the laser beams having thecharacteristics given as explained by use of FIGS. 4 to 6, FIGS. 7 to 9,and FIGS. 10 to 12 in a state that the first image forming lens 30 a orthe second image forming lens 30 b is intentionally detached.

FIG. 13 shows the relationship between an amount of defocus of the mainscanning direction (amount of change in the position of image-formation)and the position of the main scanning direction in a state that theimage forming lens 30 is detached in connection with the laser beams LY(LYa and LYb are arrayed with a predetermined distance in apredetermined sub-scanning direction). A curve FSYO shows a state thateach of the first and second image forming lenses 30 a and 30 b isdetached. A curve FSY1 shows a state that only the second image forminglens 30 b (only the first image forming lens 30 a is set) is detached. Acurve FSY2 corresponds to a state that each of image forming lenses 30 aand 30 b is set.

FIG. 14 shows the relationship between an amount of defocus of thesub-scanning direction and the position of the main scanning directionin a state that each of the image-forming lenses 30 a and 30 b isdetached in connection with the laser beams LY. A curve FSZO shows astate that each of the first and second image forming lenses 30 a and 30b is detached. A curve FSZ1 shows a state that only the second imageforming lens 30 b (only the first image forming lens 30 a is set) isdetached. A curve FSZ2 corresponds to a state that each of image forminglenses 30 a and 30 b is set.

FIG. 15 shows the relationship between an amount of a beam positioncorrection, which includes a difference between an actual position ofthe image forming in the main scanning direction and a logical positionof the image formation, and the position of the main scanning directionin connection with the laser beams LY. A curve YO shows a state thateach of the first and second image forming lenses 30 a and 30 b isdetached. A curve Y1 shows a state that only the second image forminglens 30 b (only the first image forming lens 30 a is set) is detached. Acurve Y2 corresponds to a state that each of image forming lenses 30 aand 30 b is set.

FIG. 16 shows the relationship between an amount of defocus of the mainscanning direction and the position of the main scanning direction in astate that each of the image-forming lenses 30 a and 30 b is detached inconnection with the laser beam LMa.

FIG. 17 shows the relationship between an amount of defocus of thesub-scanning direction and the position of the main scanning directionin a state that each of the image forming lenses 30 a and 30 b isdetached in connection with the laser beam LMa.

FIG. 18 shows the relationship between an amount of a beam positioncorrection, which includes a difference between an actual position ofthe image forming in the main scanning direction and a logical positionof the image formation, and the position of the main scanning directionin connection with the laser beam LMa.

FIG. 19 shows the relationship between an amount of defocus of the mainscanning direction and the position of the main scanning direction in astate that each of the image forming lenses 30 a and 30 b is detached inconnection with the laser beam LCa.

FIG. 20 shows the relationship between an amount of defocus of thesub-scanning direction and the position of the main scanning directionin a state that each of the image forming lenses 30 a and 30 b isdetached in connection with the laser beam LCa.

FIG. 21 shows the relationship between an amount of a beam positioncorrection, which includes a difference between an actual position ofthe image forming in the main scanning direction and a logical positionof the image formation, and the position of the main scanning directionin connection with the laser beam LCa.

The laser beam LBa emitted from the first black laser 3Ba hassubstantially the same characteristic as the laser beam LYa emitted fromthe first yellow laser 3Ya. For this reason, the specific explanation ofthe laser beam LBa is omitted.

As shown in FIGS. 13, 16, and 19, if the image forming lens of thepost-deflection optical lens is intentionally detached, the laser beamsL (Y, M, C, B) emitted from the light sources 3 (Y, M, C, B) areimage-formed on the portion, which is further than the image surfacewith respect to the main scanning direction by convergence provided fromthe pre-deflection optical system 7 (FSY0).

In this case, if only the first image forming lens 30 a is inserted, thelaser beam, which is passed through the center of the lens, isimage-formed on a minus side, that is, a portion close to the polygonmirror unit 5. On the other hand, the laser beam, which is passedthrough the lens end portion, is image-formed on a plus side, that is,the direction opposite to the polygonal mirror unit 5. In other words,the first image forming lens 30 a has power with which the image formingposition of the main scanning direction can be moved to the side of thepolygon mirror unit at the central portion of the lens. Also, the secondimage forming lens 30 a has a function of moving the image formingposition to the side opposite to the polygon mirror unit at the portionclose to the lens end portion (FSY1). Moreover, if the second imageforming lens 30 b is set, the laser beam, which is passed through thecenter of the first image forming lens, and the laser beam, which ispassed through the end portion, are substantially linearly image-formedon a predetermined image surface, respectively. In other words, thesecond image forming lens 30 a has power with which the image formingposition of the main scanning direction can be moved to the directionopposite to the polygon mirror unit at the central portion of the lens.Also, the second image forming lens 30 b has a function of moving theimage forming position to the polygon mirror unit at the portion closeto the end portion. That is, the second image forming lens 30 b isformed to have power, which is increased as the lens 30 b is away fromthe center of the lens with respect to the main scanning direction(FSY2). Thereby, even if the temperature and humidity are changed, theimage forming optical system (post-deflection optical system) havinglittle change of the image forming position can be provided.

As shown in FIGS. 14, 17, and 20, if the first and second image forminglenses 30 a and 30 b of the post-deflection optical system areintentionally detached, the laser beams L (Y, M, C, B) emitted from thelight sources 3 (Y, M, C, B) are image-formed on a portion close to thereflection point of each reflection surface of the polygon mirror body 5a with respect to the sub-scanning direction perpendicular to the mainscanning direction by the pre-deflection optical system 7 (FSZO). Atthis time, if only the first image forming lens 30 a is inserted, thelaser beam, which is passed through substantially the center of thelens, is image-formed on the minus side, that is, a portion much closerto the pre-deflection optical systems 7 (Y, M, C, B) than the reflectionpoint of each of the reflection surface of the polygon mirror body 5 a.In other words, the first image forming lens 30 a has a function ofmoving the image forming position of the sub-scanning direction to thedirection, which is further than the image surface. The amount ofmovement of the image forming position of the sub-scanning directionbecomes large at the central portion of the lens as compared with theend portion of the lens (FSZ1). Moreover, by inserting the second imageforming lens 30 b, the laser beam, which is passed through the center ofthe first image forming lens, and the laser beam, which is passedthrough the end portion of the lens, are substantially linearlyimage-formed on a predetermined image surface. In other words, thesecond image lens 30 b has power with which the image forming positionof the sub-scanning direction can be moved to the image surface side inthe entire area of the main scanning direction of the lens. That is, thepower of the second image forming lens 30 b of the sub-scanningdirection in the central area of the lens is set to be smaller than thelens end portion (FSZ2). Thereby, even if the amount of correctinginclination of each reflection surface of the polygon mirror body 5 a islarge and the temperature and humidity are changed, a post-deflectionoptical system having little change of the image forming position can beprovided.

As shown in FIGS. 15, 18, and 21, if the first and second image forminglenses 30 a and 30 b of the post-deflection optical system areintentionally detached, the laser beams L (Y, M, C, B), which areemitted from the light sources 3 (Y, M, C, B), and which are passedthrough the position corresponding to the center of the lens in the casein which the image forming lens 30 exists, are image-formed on apredetermined image surface (YO). In this case, if only the first imageforming lens 30 a is inserted, the laser beam, which is passed throughthe center of the lens, is image-formed at substantially the equalposition with respect to the main scanning direction of the lens. Then,the laser beam, which is passed through the lens end portion, is shiftedto the center of the lens so as to be image-formed in proportion to thedistance between the position of the main scanning direction where thelaser beams are passed and the center of the main scanning direction ofthe lens (Y1). Also, if the second image forming lens 30 b is furtherinserted, the laser beam, which is passed through the center of thelens, is image-formed at a substantially equal position with respect tothe main scanning direction of the lens. Then, the laser beam, which ispassed through the lens end portion, is further shifted to the center ofthe lens so as to be image-formed in proportion to the distance betweenthe position of the main scanning direction where the laser beams arepassed and the center of the main scanning direction of the lens (Y2).In other words, the first and second image forming lenses 30 a and 30 bhave the function of moving the laser beam to the center of the mainscanning direction with respect to the main scanning direction as thedistance of the main scanning direction from the center of the lens isincreased. The function of moving the laser beam is increased by apredetermined function as the distance of the main scanning directionfrom the center of the lens is increased. Therefore, there can beobtained a good constant velocity in deflecting the laser beam in themain scanning direction. Also, the variation of the position of the mainscanning direction caused by the change of the temperature and humiditycan be reduced.

As explained above, the optical characteristics of FIG. 1 are given tothe image forming lens 30 of the multi-beam exposer unit of FIGS. 2 and3. Thereby, as explained with reference to FIGS. 13 to 21, there can beprovided the post-deflection optical system in which the amount ofdefocus of the main scanning direction, that of the sub-scanningdirection, and the position of the laser beam of the main scanningdirection are not changed by depending on the variations of thetemperature and humidity even if two plastic lenses are used.

The first and second image forming lenses 30 a and 30 b are placed atthe position, which is defined such that the distance from thereflection point of each reflection surface of the polygon mirror body 5a is shorter than the distance from the image surface, that is, theportion close to the polygon mirror unit 5 than the center of thedistance between each reflection point of each reflection surface of thepolygon mirror body 5 a and the image surface. As a result, the size ofthe multi-beam exposer unit can be reduced.

The following will explain the first modification of the pre-deflectionoptical system of the first embodiment between the light source (laserelement) and the polygon mirror unit.

A multi-beam exposer unit 101 comprises first to fourth light sources103Y, 103M, 103C, and 103B for generating the laser beam correspondingto image data, which is color-separated into color components. Each offour light sources includes two laser elements for each color (yellow,magenta, cyan, black). Just for simplifying the explanation, thefollowing will describe the structure of the laser beam LB (black). Inthis case, the same reference numerals are added to the same structureas the structure of FIGS. 2 and 3, and the specific explanation isomitted. Since the number of the respective light sources 103 (Y, M, C,B) is Ni (Ni=positive integral number, in this case,${\left. {{{N1} = {{N2} = {{N3} = {{N4} = 2}}}},\quad {i = {1 + {0M}}},\quad {M = {{nomber}\quad {of}\quad {colors}}}} \right) = {\sum\limits_{i = 1}^{M}{Ni}}},$

it is needless to say that (Ni−$\left. 1 \right) = {{1\quad {half}\quad {mirrors}\quad 111\quad \left( {Y,M,{C\quad {and}\quad B}} \right)} = {\sum\limits_{i = 1}^{M}\left( {{Ni} - 1} \right)}}$

is used for each light source.

As shown in FIG. 22, the multi-beam exposer unit 101 comprises lightsources, that is, first and second lasers 103Ba and 103Bb, polygonmirror unit 5, pre-deflection optical systems 107Ba and 107Bb, first andsecond finite focal lenses 108Ba, 108Bb, and a half mirror 111B. Thepre-deflection optical system 107Ba is provided between the first blacklaser 103Ba and the polygon mirror unit 5 to set the cross-section beamspot of the laser beam LBa from the laser 103Ba to a predeterminedshape. The pre-deflection optical system 107Bb is provided between thesecond black laser 103Bb and the polygon mirror unit 5 to set thecross-section beam spot of the laser beam LBb from the laser 103Bb to apredetermined shape. Each of the first and second finite focal lenses108Ba and 108Bb, which is positioned to be integral with each of lasers103Ba and 103Bb, provides a predetermined convergence to each of thelaser beams LBa and LBb emitted from each laser. The half mirror 111B isused to put together the laser beams LBa and LBb as one light beam.Pre-deflection optical systems 107Ba and 107Bb can be differentiated bychecking whether or not the respective pre-deflection optical systems107Ba and 107Bb are transmitted through a half mirror 111B, or whetheror not the respective pre-deflection optical systems 107Ba and 107Bb arereflected by the half mirror 111B.

Each of mirrors 109Ba and 109Bb is provided between each of the firstand second finite focal lenses 108Ba and 108Bb and the half mirror 111B.The mirrors 109Ba and 109Bb reflect laser beams LBa and LBb, to whichthe predetermined convergence is given by the finite focal lenses 108Baand 108Bb, toward the half mirror 111B. The cylinder lens 112B, holdingmember 115, and dust prevention glass 114 are provided between the halfmirror 111B and the polygon mirror unit 5. The cylinder lens 112Bfurther converges the laser beam LB synchronized by the half mirror 111Bin only the sub-scanning direction. The holding member 115 surrounds thepolygon mirror unit 5. The dust prevention glass 114 is used togetherwith the holding member 115. Thereby, the polygon mirror body 5 a issealed, and the respective laser beams LBa, and Bb are transmitted tothe respective reflection surfaces of the polygon mirror body 5 a.

Then, the spherical aberration generated by the optical system shown intable 3 is given to the fist and second finite focal lenses 108Ba and108Bb to provide an image forming characteristic shown by FIGS. 23A and23B. In other words, the spherical aberration is used to improve thecharacteristic of the main scanning direction as the part of thecharacteristic of the sub-scanning direction provided by the firstembodiment is partially changed. In this case, equation (9) shows theshapes of the first and second finite focal lenses surfaces 108Ba and108Bb. $\begin{matrix}{{\chi = {\frac{{CH}^{2}}{1 + \sqrt{1 - {{ccC}^{2}H^{2}}}} + {adH}^{4} + {aeH}^{6} + {afH}^{8} + {{agH}^{10}\quad {in}\quad {this}\quad {case}}}},\quad {H = \sqrt{y^{2} + z^{2}}}} & (9)\end{matrix}$

TABLE 3 curvature thickness material plane 1 air plane 0.3 BK7 −0.00672512.479 air −0.078554 6.000 n = 1.7978 −0.0812677 0.020 n = 1.5036 planeair cc = 0.133716000000000 ad = −8.377423603344442D-007 ae =1.592401449469098D-008 af = 9.787118666580858D-010 ag =−9.475692204982494D-013

FIGS. 23A and 23B are graphs each showing that the image-formingposition close to the main ray and the image-forming position close tothe outermost ray in a state that first and second finite focal lensesof the multi-beam exposer unit of FIG. 22 are estimated based on thespherical aberration generated by the optical system of Table 3 so thatthe position of the image surface (surface of the photosensitive drum58) is set to 0. FIG. 23A shows the change of the image forming position(amount of defocus) of the component of the main scanning direction ofthe laser beam LB. FIG. 23B shows the change of the image formingposition of the component of the sub scanning direction of the laserbeam LB. A curve a is the image-forming position close to the chief rayand a curve b is the image-forming position close to the outermost ray.Regarding the amount of defocus, a portion close to the light source103B (polygon mirror unit 5) is negative (−).

Regarding the image forming state of the main scanning direction, asshown in FIG. 23A, in the entire area of the main scanning direction,the image-forming position close to the outermost ray is set to bepositive, and the image-forming position close to the main ray is set tobe negative. In other words, in the multi-beam exposer unit 101 of FIG.22, the horizontal magnification of the main scanning direction, whichis obtained by the combination of the pre-deflection optical system 7and the post-deflection optical system 21, is set to be negative, andthat of the sub-scanning direction is set to be positive. That is, animage surface area (entire area in this case) and a direction (the mainscanning direction in this case) are provided to the optical systemincluding the light sources 103Ba and 103Bb, pre-deflection opticalsystem 107, and the image forming lens 30 (post-deflection opticalsystem 21). In this case, the image surface area and the direction areset such that the image-forming position close to the chief ray isplaced at the light source side (outside of the photosensitive drum 58)than the surface of the photosensitive drum 58 (image surface) and thatthe image-forming position close to the outermost ray is placed at theopposite side of the light source (inner side of the photosensitive drum58) than the surface of the photosensitive drum 58 (image surface).Thereby, as compared with the multi-beam exposer unit of FIGS. 2 and 3,the characteristic of the sub-scanning direction is slightly changed,but the characteristic of the main scanning direction is improved.

The thickness tm of half mirror 111B is set to 5 mm. The half mirror 111b is inclined at 30°, to the axial direction of the laser beam LB.

As dust prevention glass 114, a parallel plate having the same materialas the half mirror 111B (BK7) and a thickness tg of 2.5 mm is used. Inthe multi-beam exposer unit 101 of FIG. 22, if the direction where thehalf mirror 111B is inclined is +, the direction where the dustprevention glass 114 and the value are −30° from equation (6). In otherwords, the dust prevention glass 114 is placed at 30° to the direction,which is opposite to the direction where the half mirror 111B isinclined. The wedge plate whose incident surface and emission surfaceare non-parallel to each other with respect to the sub-scanningdirection may be used as the dust prevention glass 114 to shift straylight (not shown), which is generated by the incident surface and theemission surface, to the sub-scanning direction.

The following will specifically explain the advantage, which is broughtabout by the dust prevention glass 114. Just for comparison, the imageforming characteristics of this first modification are shown on the samescale in each of the graphs of FIGS. 4 to 6, FIGS. 7 to 9, and FIGS. 10to 12 showing the image forming characteristics of the first embodiment.

In each of FIGS. 4 to 6 (the image forming characteristic of the laserbeam LYa from the first yellow laser 3Ya is shown, and the emissionlaser beam LBa from the first black laser 3Ba has the characteristic,which is substantially equal to the first yellow laser 3Ya), a curveDYMAXf shows the change of the maximum beam diameter of the mainscanning direction. A curve DYMINf shows the change of the minimum beamdiameter of the main scanning direction. A curve DZMAXf shows the changeof the maximum beam diameter of the sub-scanning direction. A curveDZMINf shows the change of the minimum beam diameter of the sub-scanningdirection. A curve FLRYMAXf shows the change of the maximum amount offlare of the main scanning direction. A curve FLRZMAXf shows the changeof the maximum amount of flare of the sub-scanning direction. FIGS. 7 to9 show the characteristic of the laser beam LMa from the first magentalaser 3Ma, which is omitted in FIG. 22, under the same condition asFIGS. 4 to 6. FIGS. 10 to 12 show the characteristic of the laser beamLCa from the first cyan laser 3Ca, which is omitted in FIG. 22, underthe same condition as FIGS. 4 to 6. Since the marks of the curves ofthese figures are the same as the cases of FIGS. 4 to 6, the specificexplanation is omitted.

As is obvious from FIGS. 4 to 6, FIGS. 7 to 9, and FIGS. 10 to 12, thespherical aberration is provided to the finite lenses 8Ba and 8Bb toform finite focal lenses 108Ba, 108Bb (first modification of the firstembodiment). Thereby, the image forming characteristic of the mainscanning direction, which has room to be improved, can be improved. Inother words, the width variation of the sub-scanning direction, which isoriginally small, is unchanged, and the width variation of the mainscanning direction, which is originally large, is reduced. Also, theamount of flare can be improved in the main scanning direction.

Next, the following will explain the method for optimizing the amount ofthe spherical aberrations of the finite focal lenses 108Ba and 108Bb,which are incorporated to the multi-beam exposer unit 101 of FIG. 22,from a wave surface aberration.

It is assumed that the position 170 mm away from the image surface is anemission pupil in connection with the laser beam having a Gaussiandistribution in which e⁻² beam diameter on the image surface is 50 μm.Each of FIGS. 24A, 25A, 26A, 27A, 28A, 29A, 30A, and 31A shows a wavesurface aberration coefficient and the state of the wave surfaceaberration when the optimized wave surface aberration is added to thedensity distribution and the wave surface coefficient on the emissionpupil. In FIGS. 24B, 25B, 26B, 27B, 28B, 29B, 30B, and 31B, each wavesurface aberration is replaced with the amount of defocus.

In this case, the wave surface aberration can be expressed as follows:

c ₁ x ² +c ₂ x ⁴ +c ₃ x ⁶ +c ₄ x ⁸ + . . . +c ₈ x ¹⁶(rad)  (10)

wherein x is a value, which is obtained by defining the distance fromthe main ray at the emission pupil by e⁻² beam radius, and a contracteddiameter is equal to e⁻² beam radius.

The minimum and maximum beam diameters are calculated for each wavesurface aberration shown at each of FIGS. 24A, 25A, 26A, 27A, 28A, 29A,30A, and 31A within the amount of defocus of ±2.9 mm.

In case of FIG. 24A, the minimum and maximum beam diameters are 52.60 to60.94 μm when the degree of the wave surface aberration is set to seconddegree (x²). In case of FIG. 25A, the minimum and maximum beam diametersare 60.30 to 64.00 μm when the degree of the wave surface aberration isset to fourth degree (x⁴). In case of FIG. 26A, the minimum and maximumbeam diameters are 62.20 to 64.00 μm when the degree of the wave surfaceaberration is set to sixth degree (x⁶). In case of FIG. 27A, the minimumand maximum beam diameters are 61.50 to 63.20 μm when the degree of thewave surface aberration is set to eighth degree (x⁸). In case of FIG.28A, the minimum and maximum beam diameters are 61.20 to 63.00 μm whenthe degree of the wave surface aberration is set to tenth degree (x¹⁰).In case of FIG. 29A, the minimum and maximum beam diameters are 61.10 to62.90 μm when the degree of the wave surface aberration is set totwelfth degree (x¹²). In case of FIG. 30A, the minimum and maximum beamdiameters are 60.70 to 62.70 μm when the degree of the wave surfaceaberration is set to fourteenth degree (x¹⁴). In case of FIG. 31A, theminimum and maximum beam diameters are 60.50 to 62.60 μm when the degreeof the wave surface aberration is set to sixteenth degree (x¹⁶).

In FIGS. 24A and 24B, c₁=0.00587777012848

Curve P₁ in FIG. 24A can be obtained from equation (9) as follows:

P ₁={(c ₁ x ²), (x, −1, 1)}

In FIGS. 25A and 25B, c₁ and c₂ are shown as follows:

c₁=−4.680959835990669

c₂=6.524161634311780

Curve P₂ in FIG. 25A can be obtained from equation (9) as follows:

P ₂={(c ₁ x ² +c ₂ x ⁴), (x, −1, 1)}

In FIGS. 26A and 26B, c₁, c₂, C₃ are shown as follows:

c₁=−2.326913380539070

c₂=−0.184605948401750

c₃=5.216107608502032

Curve P₃ in FIG. 26A can be obtained from equation (9) as follows:

P ₃={(c ₁ x ² +c ₂ x ⁴ +c ₃ x ⁶), (x, −1, 1)}

In FIGS. 27A and 27B, c₁, c₂, C₃, and c₄ are shown as follows:

c₁=−0.558659050233116

c₂=−1.171632940388197

c₃=−0.989319620337984

c₄=6.039418148065442

Curve P₄ in FIG. 27A can be obtained as follows:

P ₄={(c ₁ x ² +c ₂ x ⁴ +c ₃ x ⁶ +c ₄ x ⁸), (x, −1, 1)}

In FIGS. 28A and 28B, c₁, c₂, C₃, c₄, and c₅ are shown as follows:

c₁=−0.668726579771422

c₂=−0.307726562086162

c₃=−0.699563088118124

c₄=1.774129048350784

c₅=3.206003854830932

Curve P₅ in FIG. 28A can be obtained as follows:

P ₅={(c ₁ x ² +c ₂ x ⁴ +c ₃ x ⁶ +c ₄ x ⁸ +c ₅ x ¹⁰), (x, −1, 1)}

In FIGS. 29A and 29B, c₁, c₂, C₃, c₄, c₅, and c₆ are shown as follows:

c₁=−0.519076679796795

c₂=−0.831509074620663

c₃=0.553755848546272

c₄=1.014426983095962

c₅=1.313237340598540

c₆=1.770200577167844

Curve P₆ in FIG. 29A can be obtained as follows:

P ₆={(c ₁ x ² +c ₂ x ⁴ +c ₃ x ⁶ +c ₄ x ⁸ +c ₅ x ¹⁰ +C ₆ x ¹²), (x, −1,1)}

In FIGS. 30A and 30B, c₁, c₂, C₃, c₄, c₅, c₆, and c₇ are shown asfollows:

c₁=−0.507800431424249

c₂=−0.388376123162095

c₃=0.366157207180402

c₄=0.433944380660281

c₅=0.655750585204756

c₆=1.104614195605661

c₇=1.615135888818497

Curve P₇ in FIG. 30A can be obtained as follows:

 P ₇={(c ₁ x ² +c ₂ x ⁴ +c ₃ x ⁶ +c ₄ x ⁸ +c ₅ x ¹⁰ +C ₆ x ¹² +c ₇ x¹⁴), (x, −1, 1)}

In FIGS. 31A and 31B, c₁, c₂, C₃, c₄, c₅, c₆, and c₇ are shown asfollows:

c₁=−0.422615757350724

c₂=−0.346786191715331

c₃=0.322282923310823

c₄=0.396397953991157

c₅=0.392181124779868

c₆=0.639157455530054

c₇=0.968726875224168

c₈=1.311991087479074

Curve P₈ in FIG. 31A can be obtained as follows:

P ₈={(c ₁ x ² +c ₂ x ⁴ +c ₃ x ⁶ +c ₄ x ⁸ +c ₅ x ¹⁰ +C ₆ x ¹² +c ₇ x ¹⁴+c ₈ x ¹⁶), (x, −1, 1)}

From each graph, the wave surface aberration becomes smaller as the wavesurface aberration is separated from the central portion, and the wavesurface aberration is gradually increased at the peripheral portion toobtain a large value.

The relationship between a geometrical aberration and the wave surfaceaberration satisfies the following equation: $\begin{matrix}{{\delta \quad y} \propto {{- \alpha}\frac{\partial w}{\partial x}}} & (11)\end{matrix}$

Therefore, the above point shows that the image forming position (wavesurface aberration) of the beam close to the main beam is defined at theobject point than the image surface and that the image forming position(wave surface aberration) of the beam close to the outermost beam isdefined in the image surface area and the direction opposite to theobject point (+ side shows the direction of the object).

As mentioned above, if a predetermined spherical aberration, e.g., x¹⁶(sixteenth) is given to the finite lens, the maximum beam diameter canbe controlled to 62.60 μm within the amount of defocus of ±2.9 mm.

FIG. 32 shows that the beam waist diameter of the Gaussian(distribution) beam having no aberration is changed to obtain thevariation of the maximum beam diameter within the amount of defocus of±2.9 mm.

As is obvious from FIG. 32, in the Gaussian (distribution) beam havingno aberration, the maximum beam diameter can be controlled to less than100 μm within the amount of defocus of ±2.9 mm.

Therefore, as in the multi-beam exposer unit explained with reference toFIG. 22, the optimized wave surface aberration is given to the finitelens for providing a predetermined convergency to the laser beam fromthe laser. Thereby, the beam diameter can be prevented from beingenlarged at the defocus time.

FIGS. 33 to 35 show an example in which the finite lenses used in themulti-beam exposer unit of FIG. 22 is applied to the multi-beam exposerfor a single color (monochrome). In this case, i (number of laser beamsin the light source)=2, and M (number of light sources)=1. The samereference numerals are added to the same structure as the structure ofFIGS. 2 and 3 or FIG. 22, and the specific explanation is omitted.

As shown in FIGS. 33 to 35, a multi-beam exposer unit 201 comprisingonly first and second black laser elements 203Ba and 203Bb and a lightsource 203 for monochrome.

The multi-beam exposer unit 201 further comprises a pre-deflectionoptical system 207 a, a post-deflection optical system 21, first andsecond finite focal lenses 208Ba, 208Bb, and a half mirror 211. Thepre-deflection optical system 207 a is provided between the first laser203Ba and the polygon mirror unit 5 to set the cross section beam shapeof the laser beam LBa from the laser 203Ba to a predetermined shape. Thepre-deflection optical system 207 a is provided between the second laser203Bb and the polygon mirror unit 5 to set the cross section beam shapeof the laser beam LBb from the laser 203Bb to a predetermined shape.Each of the first and second finite focal lenses 208Ba and 208Bb, whichis positioned to be integral with each of lasers 203Ba and 203Bb,provides a predetermined convergence to each of the laser beams LBa andLBb emitted from each laser. The half mirror 211 is used to put togetherthe laser beams LBa and LBb as one light beam. Pre-deflection opticalsystems 207Ba and 207Bb can be differentiated by checking whether or notthe respective pre-deflection optical systems 207Ba and 207Bb aretransmitted through a half mirror 211, or whether or not the respectivepre-deflection optical systems 207Ba and 207Bb are reflected by the halfmirror 211.

The cylinder lens 12B, holding member 15, and dust prevention glass 214are provided between the half mirror 211 and the polygon mirror unit 5.The cylinder lens 12B further converges the laser beam LB synchronizedby the half mirror 211 in only the sub-scanning direction. The holdingmember 15 surrounds the polygon mirror unit 5. The dust prevention glass214 is used together with the holding member 15. Thereby, the polygonmirror body 5 a is sealed, and the respective laser beams LBa, and Bbare transmitted to the respective reflection surfaces of the polygonmirror body 5 a.

As dust prevention glass 214, a parallel plate having the same materialas the half mirror 211 (BK7) and a thickness tg of 2.5 mm is used. Inthe multi-beam exposer unit 201, if the direction where the half mirror211 is inclined is +, the direction where the dust prevention glass 214and the value are −30° from equation (6).

Similar to the explanation in FIGS. 2 and 3, and FIG. 22, the dustprevention glass 214 may be set such that the incident angle and theemission surface are inclined at a predetermined angle to thesub-scanning direction.

Next, the following will explain a second modification of thepre-deflection optical system between the light source (laser beam) andthe polygon mirror unit according to the first embodiment of the presentinvention with reference to FIG. 36.

As explained in FIGS. 2 and 3, a multi-beam exposer unit 301 has threesets of two laser elements for each of three colors (yellow, magenta,cyan), and M set of laser elements for black. That is, the multi-beamexposer unit 301 has first to fourth light sources 303Y (having firstand second yellow lasers 303Ya, 303Yb), 303M (having first and secondmagenta lasers. 303Ma, 303Mb), 303C (having first and second cyan lasers303Ca, 303Cb), and 303B (having first to fourth black lasers 303Ba,303Bb, 303Bc, 303Bd). Just for simplifying the explanation, thefollowing will describe the structure of the laser beams LB (black). Inthis case, the specific explanation of the same structure as thestructure of FIGS. 2 and 3 is omitted. In this case, the finite lensesare substantially the same as the case of FIG. 22, and a post-deflectionoptical system 321 is substantially the same as the case of FIGS. 2 and3. Due to this, the specific explanation is omitted.

A predetermined convergence characteristic is provided to the laser beamLBa from first black laser 303Ba by a finite focal lens 308Ba of apre-deflection optical system 307Ba. The laser beam LBa is reflected bya mirror 309Ba, passed through a first half mirror 311B-1 and a cylinderlens 312B, and guided to each reflection mirror of the polygonal mirrorbody 5 a.

A predetermined convergence characteristic is provided to the laser beamLBb from a second black laser 303Bb by a finite focal lens 308Bb of apre-deflection optical system 307Bb. The laser beam LBb is reflected bya mirror 309Bb, and guided to a second half mirror 311B-2.

The laser beam LBb guided to the second half mirror 31B-2 is passedthrough the mirror 311B-2, reflected by the first half mirror 311B-1,and passed through a cylinder lens 312B.

A predetermined convergence characteristic is provided to the laser beamLBc from third black laser 303Bc by a finite focal lens 308Bc of apre-deflection optical system 307Bc. The laser beam LBc is reflected bya mirror 309Bc, and guided to a third half mirror 311B-3.

The laser beam LBc guided to the third half mirror 311B-3 is passedthrough the mirror 311B-3, reflected by the second half mirror 311B-2and first half mirror 311B-1 in order, and passed through a cylinderlens 312B.

A predetermined convergence characteristic is provided to the laser beamLBd from fourth black laser 303Bd by a finite focal lens 308Bd of apre-deflection optical system 307bd. The laser beam LBd is reflected bya mirror 309Bd, and guided to a third half mirror 311B-3. In this case,the laser beam LBd is reflected by only the half mirror, and thetransmitted beam is not incident onto the polygon mirror unit 5. A comaaberration compensation plate 317 is provided at an arbitrary positionbetween the third half mirror 311B-3 and the finite focal lens 308Bd,e.g., a position between the finite focal lens 308Bd and the mirror309Bd. The coma aberration compensation plate 317 generates the samecoma aberration as the comma aberration characteristic generated wheneach of the laser beams LBa, LBb, and LBc. The laser beam LBd guided tothe third half mirror 311B-3 is passed through the coma aberrationcompensation plate 317, and reflected by the third half mirror 311B-3.

The laser beam LBd reflected by the third half mirror 311B-3 isreflected by the mirror 311B-3. The laser beam LBd is further guided tothe second half mirror 311B-2, and guided to the first half mirror311B-1.

The laser beam LBd guided to the first half mirror 311B-1 is furtherreflected by the mirror 311B-1, and guided to the cylinder lens 312B.

A holding member 315, and dust prevention glass 314 are provided betweenthe cylinder lens 312B and the polygon mirror unit 5. The holding member315 is surrounded around the polygon mirror unit 5. The dust preventionglass 314 is used together with the holding member 315. Thereby, thepolygon mirror body 5 a is sealed, and all laser beams LBa, Bb, LBc, andLBd, LYa, LYb, LMa, LMb, LCa, and LCb are transmitted to the respectivereflection surfaces of the polygon mirror body 5 a. The respective laserbeams, to which convergence is provided to only sub-scanning directionby the cylinder lens 312B, are passed through the dust prevention glass314, and guided to each reflection surface of the polygon mirror body 5a.

The following will specifically explain the half mirrors 311B-1, 311B-2,311B-3, the dust prevention glass 314, and the coma aberrationcompensation plate 317.

The first half mirror 311B-1 is formed to have a thickness tm-1 of 5 mm.The first half mirror 311B-1 is placed to be inclined at 30° such that aportion shown by a dotted line of laser beam LBa is incident late ascompared with a perpendicular incident time.

The second half mirror 311B-2 is formed to have a thickness tm-2 of 5mm. The second half mirror 311B-2 is placed to be inclined at 30° in thesame direction as the direction where the half mirror 311B-1 is inclinedseeing from the beam passing through the half mirror 311B-2 such that aportion shown by a dotted line of laser beam LBb is incident late ascompared with a perpendicular incident time.

The third half mirror 311B-3 is formed to have a thickness tm-3 of 5 mm.The third half mirror 311B-3 is placed to be inclined at 30° insubstantially the same direction as the direction where the half mirror311B-1 is inclined seeing from the beam passing through the half mirror311B-3 such that a portion shown by a dotted line of laser beam LBc isincident late as compared with a perpendicular incident time.

In other words, the phases of the beams passing through the half mirrors311B-2 and 311B-3 are symmetrical to the center of the beam. The beampassing through the half mirror 311B-3 is reflected by the half mirror311B-2, and further reflected by the half mirror 311B-1 so as to beoverlaid on the beam passed through the half mirror 311B-1. The beampassing through the half mirror 311B-2 is reflected by only the halfmirror 311B-1 so as to be overlaid on the beam passed through the halfmirror 311B-1. That is, the beam passing through the half mirror 311B-2must be placed to have an opposite phase to the beam passing through thehalf mirror 311B-3.

The coma aberration compensation plate 317 is formed of substantiallythe same material as each of the half mirrors 311B, e.g., thickness tpof 5 mm (BK7). The coma aberration compensation plate 317 is placed tobe inclined at 30° such that a portion shown by a dotted line of laserbeam LBd is incident late as compared with a perpendicular incidenttime. In other words, the respective first to third laser beams LBa,LBb, and LBc are passed through the half mirror only one time untilbeing made incident on the cylinder lens 312. The fourth laser beam LBdis guided to the cylinder lens 312 without transiting through theparallel plate. Therefore, the fourth laser beam LBd is transmittedthrough the parallel plate having the characteristic corresponding tothe half mirror so as to provide the coma aberration, which is equal tothe coma aberration, which is provided to each of the first to thirdlaser beams LBa, LBb, LBc from each of the half mirror. Thereby, allcoma aberrations are equal.

The dust prevention glass 314 is formed of the material, which is equalto the material of each half mirror (e.g. BK7), to have a thickness tgof 5 mm. The dust prevention glass 314 is placed to be inclined at 30°such that a portion, shown by a dotted line, of the laser beam isincident early as compared with a perpendicular incident time. The dustprevention glass 314 may be formed of the wedge plate, which is slightlyinclined in the sub-scanning direction as in the other explainedexamples.

Next, the following will specifically explain the advantage, which isbrought about by the dust prevention glass 314. In this case, just forcomparison, the image forming characteristics of this first modificationare shown on the same scale in each of the graphs of FIGS. 4 to 6, FIGS.7 to 9, and FIGS. 10 to 12 showing the image forming characteristics ofthe first embodiment.

In each of FIGS. 4 to 6 (the image forming characteristic of the laserbeam LYa from the first yellow laser 3Ya is shown, and the emissionlaser beam LBa from the first black laser 3Ba has the characteristic,which is substantially equal to the first yellow laser 3Ya), a curveDYMAXg shows the change of the maximum beam diameter of the mainscanning direction. A curve DYMINg shows the change of the minimum beamdiameter of the main scanning direction. A curve DZMAXg shows the changeof the maximum beam diameter of the sub-scanning direction. A curveDZMINg shows the change of the minimum beam diameter of the sub-scanningdirection. A curve FLRYMAXg shows the change of the maximum amount offlare of the main scanning direction. A curve FLRZMAXg shows the changeof the maximum amount of flare of the sub-scanning direction. FIGS. 7 to9 show the characteristic of the laser beam LMa from the first magentalaser 303Ma, which is omitted in the figure, under the same condition asFIGS. 4 to 6. FIGS. 10 to 12 show the characteristic of the laser beamLCa from the first cyan laser 303Ca, which is omitted in FIG. 36, underthe same condition as FIGS. 4 to 6. Since the marks of the curves ofthese figures are the same as the cases of FIGS. 4 to 6, the specificexplanation is omitted.

As is obvious from FIGS. 4 to 6, FIGS. 7 to 9, and FIGS. 10 to 12,according to the multi-beam exposer unit 301 of FIG. 36, the imageforming characteristic of the main scanning direction, which has room tobe improved in the first embodiment (FIGS. 2 and 3), can be improved.Also, the amount of flare can be entirely improved in both main andsub-scanning directions.

Next, the following will explain a third modification of thepre-deflection optical system between the light source (laser beam) andthe polygon mirror unit according to the first embodiment of the presentinvention with reference to FIG. 37.

As explained in FIGS. 2 and 3, a multi-beam exposer unit 401 has threesets of two laser elements for each of three colors (yellow, magenta,cyan), and M set of laser elements for black. That is, the multi-beamexposer unit 401 has first to fourth light sources 403Y (having firstand second yellow lasers 403Ya, 403Yb), 403M (having first and secondmagenta lasers 403Ma, 403Mb), 403C (having first and second cyan lasers403Ca, 403Cb), and 403B (having first to fourth black lasers 403Ba,403Bb, 403Bc, 403Bd). Just for simplifying the explanation, thefollowing-will describe the structure of the laser beams LB (black). Inthis case, the specific explanation of the same structure as thestructure of FIGS. 2 and 3, FIG. 22, and 36 is omitted. In this case,the finite lenses are substantially the same as the case of FIG. 22, anda post-deflection optical system 321 is substantially the same as thecase of FIGS. 2 and 3. Due to this, the specific explanation is omitted.

A predetermined convergence characteristic is provided to the laser beamLBa from first black laser 403Ba by a finite focal lens 408Ba of apre-deflection optical system 407Ba. The laser beam LBa is passedthrough a coma aberration compensation plate 417B-1, and guided to amirror 409Ba. The laser guided to the mirror 409Ba is passed through afirst half mirror 411B-1 and a cylinder lens 412B, and guided to eachreflection mirror of the polygonal mirror body 5 a.

A predetermined convergence characteristic is provided to the laser beamLBb from second black laser 403Bb by a finite focal lens 408Bb of apre-deflection optical system 407Bb. The laser beam LBb is passedthrough a coma aberration compensation plate 417B-2, and guided to themirror 409Bb. The laser beam Bb guided to the mirror 409Bb is reflectedby the mirror 409Bb, and guided to a second half mirror 411B-2.

The laser beam LBb guided to the second half mirror 411B-2 is passedthrough the mirror 411B-2, reflected by the first half mirror 411B-1,and passed through a cylinder lens 412B.

A predetermined convergence characteristic is provided to the laser beamLBc from third black laser 403Bc by a finite focal lens 408Bc of apre-deflection optical system 407Bc. The laser beam LBc is passedthrough a coma aberration compensation plate 417B-3 and reflected by amirror 409Bc, and guided to a third half mirror 411B-3.

The laser beam LBc guided to the third half mirror 411B-3 is passedthrough the mirror 411B-3, reflected by the second half mirror 411B-2and first half mirror 411B-1 in order, and passed through a cylinderlens 412B.

A predetermined convergence characteristic is provided to the laser beamLBd from fourth black laser 403Bd by a finite focal lens 408Bd of apre-deflection optical system 407 bd. The laser beam LBd is reflected bythe mirror 409Bd, third half mirror 411B-3, second half mirror 411B-2,and first half mirror 411B-1 so as to be made incident on the cylinderlens 412. Therefore, the laser beam LBd from the laser 403Bd is guidedto the polygon mirror unit 5 without being passed through the comaaberration compensation plate and the half mirror.

The following will specifically explain the coma aberration compensationplates 417B-1, 417B-2, 417B-3, and the half mirrors 411B-1, 411B-2, andthe 411B-3.

The first coma aberration compensation plate 417B-1 is formed to have athickness tp-1 of 5 mm. The first coma aberration compensation plate417B-1 is placed to be inclined at 30° to a direction where a portionshown by a dotted line of laser beam LBa is incident early as comparedwith a perpendicular incident time.

The second coma aberration compensation plate 417B-2 is formed to have athickness tp-2 of 5 mm. The second coma aberration compensation plate417B-2 is placed to be inclined at 30° to a direction where a portionshown by a dotted line of laser beam LBb is incident early as comparedwith a perpendicular incident time, that is, the same direction as thedirection where the first coma aberration compensation plate 417B-1 isinclined, seeing from the transmission beam.

The third coma aberration compensation plate 417B-3 is formed to have athickness tp-3 of 5 mm. The third coma aberration compensation plate417B-3 is placed to be inclined at 30° to a direction where a portionshown by a dotted line of laser beam LBc is incident early as comparedwith a perpendicular incident time, that is, the same direction as thedirection where the first coma aberration compensation plate 417B-1 isinclined.

The first half mirror 411B-1 is formed to have a thickness tm-1 of 5 mm.The first half mirror 411B-1 is placed to be inclined at 30° to adirection where a portion shown by a dotted line of laser beam LBapassing therethrough is incident late as compared with a perpendicularincident time. Therefore, the laser beam LBa emitted from the laser403Ba is transmitted through the coma aberration compensation plate417B-1 and the half mirror 411B-1, which are inclined to the oppositedirection to each other, and guided to the polygon mirror unit 5. Inthis case, to clarify the inclination of the coma aberrationcompensation plate 417B-1 and the half mirror 411B-1, the beam passingthrough the coma aberration compensation plate 417B-1 is shown as astraight line by a dotted line in a state that the mirror 409Ba isomitted.

The second half mirror 411B-2 is formed to have a thickness tm-2 of 5mm. The first half mirror 411B-2 is placed to be inclined at 30° to adirection where a portion shown by a dotted line of laser beam LBb isincident late as compared with a perpendicular incident time, that is,the same direction as the direction where the first half mirror 411B-1is inclined. Therefore, the laser beam LBb emitted from the laser 403Bbis transmitted through the coma aberration compensation plate 417B-2 andthe half mirror 411B-2, which are inclined to the opposite direction toeach other, and guided to the polygon mirror unit 5. In this case, toclarify the inclination of the coma aberration compensation plate 417B-2and the half mirror 411B-2, the beam passing through the coma aberrationcompensation plate 417B-2 is shown as a straight line by a dotted linein a state that the mirror 409Bb is omitted.

The second half mirror 411B-3 is formed to have a thickness tm-3 of 5mm. The first half mirror 411B-3 is placed to be inclined at 30° to adirection where a portion shown by a dotted line of laser beam LBc isincident late as compared with a perpendicular incident time, that is,the same direction as the direction where the first half mirror 411B-1is inclined. Therefore, the laser beam LBc emitted from the laser 403Bcis transmitted through the coma aberration compensation plate 417B-3 andthe half mirror 411B-3, which are inclined to the opposite direction toeach other, and guided to the polygon mirror unit 5. In this case, toclarify the inclination of the coma aberration compensation plate 417B-3and the half mirror 411B-3, the beam passing through the coma aberrationcompensation plate 417B-3 is shown as a straight line by a dotted linein a state that the mirror 409Bc is omitted.

Next, the following will specifically explain the advantages, which arebrought about by the multi-beam exposer unit 401 of FIG. 37.

According to the multi-beam exposer unit 401, the respective laser beamsguided to the polygon mirror unit 5 are passed through each comaaberration compensation plate and each half mirror, which are inclinedto be opposite to each other. The image forming characteristic of themain scanning direction, which has room to be improved in the firstembodiment (FIGS. 2 and 3), can be improved. Also, the amount of flarecan be improved in both the main and sub-scanning directions. In thiscase, just for comparison, the image forming characteristics of thisfirst modification are shown on the same scale in each of the graphs ofFIGS. 4 to 6, FIGS. 7 to 9, and FIGS. 10 to 12 showing the image formingcharacteristics of the first embodiment.

In each of FIGS. 4 to 6 (the image forming characteristic of the laserbeam LYa from the first yellow laser 3Ya is shown, and the emissionlaser beam LBa from the first black laser 3Ba has the characteristic,which is substantially equal to the first yellow laser 3Ya), a curveDYMAXh shows the change of the maximum beam diameter of the mainscanning direction. A curve DYMINh shows the change of the minimum beamdiameter of the main scanning direction. A curve DZMAXh shows the changeof the maximum beam diameter of the sub-scanning direction. A curveDZMINh shows the change of the minimum beam diameter of the sub-scanningdirection. A curve FLRYMAXh shows the change of the maximum amount offlare of the main scanning direction. A curve FLRZMAXh shows the changeof the maximum amount of flare of the sub-scanning direction. FIGS. 7 to9 show the characteristic of the laser beam LMa from the first magentalaser 3Ma, which is omitted in the figure, under the same condition asFIGS. 4 to 6. FIGS. 10 to 12 show the characteristic of the laser beamLCa from the first cyan laser 3Ca, which is omitted in FIG. 37, underthe same condition as FIGS. 4 to 6. Since the marks of the curves ofthese figures are the same as the cases of FIGS. 4 to 6, the specificexplanation is omitted.

Next, the following will explain a fourth modification of thepre-deflection optical system between the light source (laser beam) andthe polygon mirror unit according to the first embodiment of the presentinvention with reference to FIG. 38.

As explained in FIGS. 2 and 3, a multi-beam exposer unit 501 has threesets of two laser elements for each of three colors (yellow, magenta,cyan), and M sets of laser elements for black. That is, the multi-beamexposer unit 501 has first to fourth light sources 503Y (having firstand second yellow lasers 503Ya, 503Yb), 503M (having first and secondmagenta lasers 503Ma, 503Mb), 503C (having first and second cyan lasers503Ca, 503Cb), and 503B (having first to fourth black lasers 503Ba,503Bb, 503Bc, 503Bd). Just for simplifying the explanation, thefollowing will describe the structure of the laser beams LB (black). Inthis case, the specific explanation of the same structure as thestructure of FIGS. 2 and 3, FIG. 22, is omitted. In this case, thefinite lenses are substantially the same as the case of FIG. 22, and apost-deflection optical system 321 is substantially the same as the caseof FIGS. 2 and 3. Due to this, the specific explanation is omitted.

A predetermined convergence characteristic is provided to the laser beamLBa from first black laser 503Ba by a finite focal lens 508Ba of apre-deflection optical system 507Ba. The laser beam LBa is reflected bythe mirror 509Ba, passed through a first half mirror 511B-1 and acylinder lens 512B, and guided to each reflection mirror of thepolygonal mirror body 5 a.

A predetermined convergence characteristic is provided to the laser beamLBb from second black laser 503Bb by a finite focal lens 508Bb of apre-deflection optical system 507Bb. The laser beam LBb is reflected bythe mirror 509Bb, and guided to a second half mirror 511B-2. The laserbeam LBb guided to the second half mirror 511B-2 is passed through themirror 511B-2, reflected by the first half mirror 511B-1, and passedthrough the cylinder lens 512B.

A predetermined convergence characteristic is provided to the laser beamLBc from third black laser 503Bc by a finite focal lens 508Bc of apre-deflection optical system 507Bc. The laser beam LBc is reflected bythe mirror 509Bc, and guided to a third half mirror 511B-3. The laserbeam LBc guided to the third half mirror 511B-3 is passed through themirror 511B-3, reflected by the second half mirror 511B-2 and the firsthalf mirror 511B-1 in order, and passed through the cylinder lens 512B.

A predetermined convergence characteristic is provided to the laser beamLBb from fourth black laser 503Bd by a finite focal lens 508Bd of apre-deflection optical system 507Bd. The laser beam LBd is reflected bythe mirror 509Bd, and guided to the third half mirror 511B-3. The laserbeam LBd guided to the third half mirror 511B-3 is reflected by themirror 511B-3, further reflected by the second half mirror 511B-2, andguided to the first half mirror 511B-1.

The laser beam LBd guided to the first half mirror 511B-1 is reflectedby the mirror 511B-1 to be incident on the cylinder lens 512B.

A holding member 515, and dust prevention glass 514 are provided betweenthe cylinder lens 512B and the polygon mirror unit 5. The holding member515 surrounds the polygon mirror unit 5. The dust prevention glass 514is used together with the holding member 515. Thereby, the polygonmirror body 5 a is sealed, and all laser beams LBa, Bb, LBc, and LBd,LYa, LYb, LMa, LMb, LCa, and LCb are transmitted to the respectivereflection surfaces of the polygon mirror body 5 a. The respective laserbeams, to which convergence is provided to only the sub-scanningdirection by the cylinder lens 512B, are passed through the dustprevention glass 514, and guided to each reflection surface of thepolygon mirror body 5 a.

The following will specifically explain the half mirrors 511B-1, 511B-2,51B-3, and the dust prevention glass 514.

The first half mirror 511B-1 is formed to have a thickness tm-1 of 5 mm.The first half mirror 511B-1 is placed to be inclined at 30° such that aportion shown by a dotted line of laser beam LBa is incident late ascompared with a perpendicular incident time.

The second half mirror 511B-2 is formed to have a thickness tm-2 of 5mm. The second half mirror 511B-2 is placed to be inclined at 30° in thesame direction as the direction where the half mirror 511B-1 is inclinedsuch that a portion shown by a dotted line of laser beam LBb is incidentlate as compared with a perpendicular incident time.

The third half mirror 511B-3 is formed to have a thickness tm-3 of 5 mm.The third half mirror 511B-3 is placed to be inclined at 30° insubstantially the same direction as the direction where the half mirror511B-1 is inclined such that a portion shown by a dotted line of laserbeam LBc is incident late as compared with a perpendicular incidenttime.

The dust prevention glass 514 is formed of the material, which is equalto the material of each of half mirrors 511B-1, 511B-2, 511B-3 (e.g.BK7), to have a thickness tg of 2.5 mm. The dust prevention glass 514 isplaced to be inclined at 30° in the direction, which is opposite to thedirection where the first half mirror 511B-1 is inclined, that is, thedirection where a portion shown by a dotted line of laser beam isincident early as compared with a perpendicular incident time. In otherwords, the dust prevention glass 514 is placed between the polygonmirror body 5 a and the cylinder lens 512 to satisfy equation (6). Thedust prevention glass 514 may be formed of the wedge plate, which isslightly inclined in the sub-scanning direction as in the otherexplained examples.

The image forming characteristic, which is obtained by the dustprevention glass 514, substantially conforms to the image formingcharacteristic, which is obtained by the multi-beam exposed unit 301 ofFIG. 36. Due to this, the specific explanation is omitted. Specifically,in FIGS. 4 to 6, FIGS. 7 to 9, and FIGS. 10 to 12, a curve DYMAXhg showsthe change of the maximum beam diameter of the main scanning direction.A curve DYMINg shows the change of the minimum beam diameter of the mainscanning direction. A curve DZMAXg shows the change of the maximum beamdiameter of the sub-scanning direction. A curve DZMINg shows the changeof the minimum beam diameter of the sub-scanning direction. A curveFLRYMAXg shows the change of the maximum amount of flare of the mainscanning direction. A curve FLRZMAXg shows the change of the maximumamount of flare of the sub-scanning direction.

Next, the following will specifically explain a first modification ofthe post-deflection optical system of the second embodiment withreference to FIG. 39. In this case, Tables 4 and 5 show the specificcharacteristics.

As shown in FIG. 39, a post-deflection optical system of a multi-beamexposer unit 601 has a set of image forming lenses 630 including firstand second image forming lenses 630 a and 630 b, and having opticalcharacteristics and shapes as shown in the following Tables 4 and 5 andequation (8). Each of the image forming lenses 630 a and 630 b is placedat a predetermined position, which is defined such that the distancefrom the reflection point of each reflection surface of the polygonmirror body is shorter than the distance from the image surface.

TABLE 4 absolute coordinates: Decentering Post-deflection optical systemin y direction −4.333 curvature lens surface CUY CUZ Thickness numbermaterial 0.0191994 −0.01398596 −35.435 1 air 0.0203530 0.017623888−6.524 2 PMMA 0.00207745 −0.007525851 −106.530 3 air 0.001930200.014554485 −6.0077405 4 PMMA plane plane −9.0000 air plane plane −2.000BK7 plane plane −164.000 air

TABLE 5 Lens surface number:1 n\m 0 1 2 3 4 5 0 0.000E+00 −1.024E−010.000E+00 4.199E−05 −4.956E−06 −8.504E−09 1 0.000E+00 −1.946E−042.901E−06 3.304E−07 1.117E−08 −8.850E−10 2 −1.117E−04 −6.301E−06−4.111E−08 5.560E−08 −3.078E−09 3.062E−11 3 1.011E−05 2.747E−07−8.713E−10 −2.335E−09 1.490E−10 −1.090E−12 4 −2.274E−07 −4.250E−09−1.708E−10 3.997E−11 −1.133E−12 0.000E+00 n\m 6 7 8 9 10 0 −1.003E−103.167E−11 −5.521E−13 −1.391E−14 5.931E−16 1 6.295E−12 −5.949E−131.447E−14 9.629E−16 −2.351E−17 2 4.215E−12 −2.093E−13 4.220E−15−2.127E−16 5.852E−18 3 −9.385E−14 −5.320E−15 −1.699E−16 3.985E−17−8.949E−19 4 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 Lenssurface number:2 n\m 0 1 2 3 4 5 0 0.000E+00 −1.099E−01 0.000E+002.775E−05 −4.312E−06 7.028E−09 1 0.000E+00 −1.800E−04 3.170E−073.155E−07 −1.710E−09 −4.400E−10 2 −2.347E−05 −6.470E−06 −8.468E−094.092E−08 −7.745E−10 −1.563E−11 3 −3.233E−06 3.825E−07 −5.645E−09−2.683E−09 9.429E−11 3.540E−12 4 −1.497E−05 5.495E−02 1.268E−06−1.386E−05 2.156E−06 −2.284E−08 n\m 6 7 8 9 10 0 −6.980E−10 1.143E−11−1.355E−13 −3.441E−15 2.118E−16 1 1.821E−11 −6.661E−13 8.933E−15−2.343E−16 8.749E−18 2 −1.504E−12 −2.969E−14 2.727E−15 1.337E−16−4.583E−18 3 −3.149E−14 −7.475E−15 2.478E−17 3.870E−18 6.668E−21 42.167E−09 −3.695E−11 4.422E−13 9.386E−15 −6.004E−16 Lens surfacenumber:3 n\m 0 1 2 3 4 5 0 0.000E+00 1.296E−02 0.000E+00 −3.605E−06−1.849E−07 2.323E−10 1 0.000E+00 −2.439E−05 6.051E−07 −1.086E−098.291E−11 3.939E−14 2 −6.396E−06 −3.822E−08 6.691E−11 1.398E−11−8.191E−15 −4.383E−16 3 1.785E−09 1.367E−10 2.198E−12 5.493E−14−4.323E−16 2.107E−18 4 1.431E−10 −5.451E−13 −2.146E−14 2.674E−18−5.170E−18 0.000E+00 n\m 6 7 8 9 10 0 1.594E−11 2.401E−14 −7.621E−161.189E−18 −1.349E−20 1 −1.416E−14 6.108E−17 −5.136E−19 1.941E−211.858E−23 2 2.442E−17 −6.388E−19 1.625E−21 3.775E−23 −1.673E−25 31.372E−19 −5.140E−22 6.187E−24 −2.356E−26 −1.057E−27 4 0.000E+000.000E+00 0.000E+00 0.000E+00 0.000E+00 Lens surface number:4 n\m 0 1 23 4 5 0 0.000E+00 7.011E−03 0.000E+00 −4.689E−06 −3.578E−08 4.162E−10 10.000E+00 −1.836E−05 3.311E−07 −2.139E−09 4.244E−11 1.662E−13 2−7.224E−06 −3.965E−08 2.930E−10 1.361E−11 1.098E−15 −1.857E−15 3−1.843E−09 8.047E−11 1.719E−13 5.319E−14 2.651E−16 3.381E−18 4 1.054E−10−3.327E−13 −5.079E−16 3.219E−17 −7.436E−18 0.000E+00 n\m 6 7 8 9 10 02.683E−12 −1.290E−14 3.640E−16 4.272E−18 −6.504E−20 1 3.689E−168.861E−18 −1.510E−18 9.122E−21 −5.947E−24 2 2.850E−18 −5.879E−203.260E−21 −1.337E−23 −9.839E−26 3 8.933E−20 −5.736E−22 −4.127E−24−5.205E−26 5.705E−28 4 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

FIGS. 40 to 42 are graphs showing a state that the laser beam LC isimage-formed by a post-deflection optical system 621 to which theoptical characteristics of Tables 4 and 5 are provided. Similar to thecase explained in FIGS. 10 to 12, each graph shows that the first imageforming lens 630 a or the second image forming lens 630 b, or bothlenses are intentionally detached, so that the image formingcharacteristic is improved. The specific explanation of each of thelaser beams LB, LY, and LM is omitted since the results, which aresimilar to the second embodiment shown in FIGS. 13 to 15 and FIGS. 16 to18, can be obtained.

FIG. 40 is a graph showing the relationship between an amount of defocus(change of image-formation position) of the main scanning direction andthe position of the main scanning direction in a state that the imageforming lenses 630 are detached in connection with the laser beams LM(LMa and LMb are arrayed to have a predetermined distance in thesub-scanning direction). In this case, a curve FSY0 shows that each offirst and second image forming lenses 630 a and 630 b is detached. Acurve FSY1 shows that only the second image forming lens 630 b isdetached (only the first image forming lens 630 a is used). A curve FSY2corresponds to a state that each of the first and second lenses 630 aand 630 b is set.

FIG. 41 is a graph showing the relationship between an amount of defocusof the sub-scanning direction and the position of the main scanningdirection in a state that the image-forming lens is detached inconnection with the laser beams LM.

In this case, a curve FSZ0 shows that each of first and second imageforming lenses 630 a and 630 b is detached. A curve FSZ1 shows that onlythe second image forming lens 630 b is detached (only the first imageforming lens 630 a is used). A curve FSZ2 corresponds to a state thateach of the first and second lenses 630 a and 630 b is set.

FIG. 42 is a graph showing the relationship between an amount of a beamposition correction, which includes a difference between an actualposition of the image-forming in the main scanning direction and alogical position of the image formation, and the position of the mainscanning direction in connection with the laser beams LM. In this case,a curve Y0 shows that each of first and second image forming lenses 630a and 630 b is detached. A curve Y1 shows that only the second imageforming lens 630 b is detached (only the first image forming lens 630 ais used). A curve Y2 corresponds to a state that each of the first andsecond lenses 630 a and 630 b is set.

As shown in FIG. 40, if each of first and second image forming lenses630 a and 630 b is detached, the laser beam emitted from the lightsource is image-formed on a portion further than the image surface withrespect to the main scanning direction by the pre-deflection opticalsystem 607 (FSY0). If only the first image forming lens 630 a isinserted, the laser beam, which passes through a portion close to thecenter of the image forming lens 630 a, is image-formed on a portionclose to the polygon mirror unit 5 than FY0. The laser beam, whichpasses through a portion close the end portion of the image forming lens630 a, is image-formed on a portion opposite to the polygon mirror unit5 than FSY0. In other words, at the portion close to the center of thelens, the first image forming lens 630 a has power with which the imageforming position of the main scanning direction can be moved to thepolygon mirror unit. At the portion close to the end portion of thelens, the first image forming lens 630 a has a function of moving theimage forming position to the portion opposite to the polygon mirrorunit (FSY1).

If the second image forming lens 630 b is set, the laser beam, whichpasses through a portion close to the center of the image forming lens630 a, and the laser beam, which passes through a portion close the endportion of the image forming lens 630 a, are substantially linearlyimage-formed on a predetermined image surface, respectively. In otherwords, at the portion close to the center of the lens, the second imageforming lens 630 b has power with which the image forming position ofthe main scanning direction can be moved to a portion to the polygonmirror unit. At the portion close to the end portion of the lens, thesecond image forming lens 630 b has a greater function of moving theimage forming position to the polygon mirror unit. In other words, thesecond image forming lens 630 b is formed to have power, which isincreased as the lens 630 b is away from the center of the lens withrespect to the main scanning direction (FSY2). Thereby, even if thetemperature and humidity are changed, there can be provided thepost-deflection optical system having little change of the image formingposition.

As shown in FIG. 41, if the first and second image forming lenses 630 aand 630 b of the post-deflection optical system 621 are intentionallydetached, the laser beams emitted from the light sources 3 areimage-formed on a portion close to the reflection point of eachreflection surface of the polygon mirror body Sa with respect to thesub-scanning direction perpendicular to the main scanning direction(FSZ0). At this time, if only the first image forming lens 630 a isinserted, the laser beam, which is passed through substantially thecenter of the lens, is image-formed on a portion much closer to thepre-deflection optical system than the reflection point of each of thereflection surface of the polygon mirror body 5 a. In other words, thefirst image forming lens 630 a has a function of moving the imageforming position to the direction, which is further than the imagesurface. The amount of the movement of the image forming position of thesub-scanning direction becomes large at the central portion of the lensas compared with the end portion of the lens (FSZ1). Moreover, by theinsertion of the second image forming lens 630 b, the laser beam, whichis passed through the center of the first image forming lens, and thelaser beam, which is passed through the end portion of the lend, aresubstantially linearly image-formed on a predetermined image surface,respectively. In other word, the second image lens 630 b has power withwhich the image forming position of the sub-scanning direction can bemoved to the image surface side in the entire area of the main scanningdirection of the lens. That is, power of the second image forming lens630 b of the sub-scanning direction in the central area of the lens isset to be smaller than the lens end portion (FSZ2). Thereby, even if theamount of correcting inclination of each reflection surface of thepolygon mirror body 5 a is large and the temperature and humidity arechanged, post-deflection optical system having little change of theimage forming position can be provided.

As shown in FIG. 42, if the first and second image forming lenses 630 aand 630 b of the post-deflection optical system are intentionallydetached, the laser beams, which are emitted from the light sources, andwhich are passed through the position corresponding to the center of thelens in the case in which the image forming lens 630 exists, areimage-formed on a predetermined image surface (Y0). In this case, ifonly the first image forming lens 630 a is inserted, the laser beam,which is passed through the center of the lens, is image-formed atsubstantially the equal position with respect to the main scanningdirection of the lens. Then, the laser beam, which is passed through thelens end portion, is shifted to the center of the lens so as to beimage-formed in proportion to the distance between the position of themain scanning direction where the laser beams are passed and the centerof the main scanning direction of the lens (Y1). Also, if the secondimage forming lens 630 b is further inserted, the laser beam, which ispassed through the center of the lens, is image-formed at substantiallythe equal position with respect to the main scanning direction of thelens. Then, the laser beam, which is passed through the lens endportion, is further shifted to the center of the lens so as to beimage-formed in proportion to the distance between the position of themain scanning direction where the laser beams are passed and the centerof the main scanning direction of the lens (Y2). In other words, thefirst and second image forming lenses 630 a and 630 b have the functionof moving the laser beam to the center of the main scanning directionwith respect to the main scanning direction as the distance of the mainscanning direction from the center of the lens is increased. Thefunction of moving the laser beam is increased by a predeterminedfunction as the distance of the main scanning direction from the centerof the lens is increased. Therefore, there can be obtained a goodconstant velocity in deflecting the laser beam in the main scanningdirection. Also, the variation of the position of the main scanningdirection caused by the change of the temperature and humidity can bereduced.

As explained above, the optical characteristics of Tables 4 and 5 aregiven to the image forming lens 630 of the multi-beam exposer unit 601including the optical elements similar to the multi-beam exposer unit ofFIGS. 2 and 3. Thereby, as explained with reference to FIGS. 39 to 41,there can be provided the post-deflection optical system in which theamount of defocus of the main scanning direction, that of thesub-scanning direction, and the position of the laser beam of the mainscanning direction are not changed by depending on the variations of thetemperature and humidity even if two plastic lenses are used.

The first and second image forming lenses 630 a and 630 b are placed atthe position, which is defined such that the distance from thereflection point of each reflection surface of the polygon mirror body 5a is shorter than the distance from the image surface, that is, theportion close to the polygon mirror unit 5 than the center of thedistance between each reflection point of each reflection surface of thepolygon mirror body 5 a and the image surface. As a result, the size ofthe multi-beam exposer unit can be reduced.

Next, the following will specifically explain a second modification ofthe post-deflection optical system of the second embodiment withreference to FIG. 43. In this case, Tables 6 and 7 show the specificcharacteristics.

As shown in FIG. 43, a post-deflection optical system of a multi-beamexposer unit 701 has a set of image forming lenses 730 including firstand second image forming lenses 730 a and 730 b, and having opticalcharacteristics and shapes as shown in the following Tables 6 and 7 andequation (8). Each of the image forming lenses 730 a and 730 b is placedat a predetermined position, which is defined such that the distancefrom the reflection point of each reflection surface of the polygonmirror body is shorter than the distance from the image surface.

TABLE 6 absolute coordinates: Decentering Post-deflection optical systemin y direction −4.333 curvature lens surface CUY CUZ Thickness numbermaterial 0.012947194 −0.00915104 −57.652 1 air 0.0131721655 0.01124333−6.000 2 PMMA 0.000641449 −0.00414556 −166.861 3 air 0.0019876230.01029169 −6.000 4 PMMA plane plane −13.500 air plane plane −2.000 BK7plane plane −246.000 air

TABLE 7 Lens surface number:1 n\m 0 1 2 3 4 5 0 0.000E+00 −5.003E−020.000E+00 1.304E−05 −1.543E−06 −7.384E−10 1 0.000E+00 1.293E−051.241E−07 −1.873E−08 3.377E−09 −4.487E−11 2 −8.657E−05 −1.757E−07−1.539E−07 6.546E−09 −1.282E−11 1.168E−12 3 3.980E−06 3.008E−092.039E−09 −2.018E−10 9.121E−12 −4.024E−13 4 −6.088E−08 −5.508E−10−4.943E−12 7.324E−12 −2.132E−13 0.000E+00 n\m 6 7 8 9 10 0 −5.779E−112.473E−12 −4.780E−14 −4.259E−16 2.275E−17 1 1.062E−12 −5.393E−14−1.745E−18 1.044E−18 8.562E−19 2 1.578E−13 −8.972E−15 −8.407E−17−3.526E−18 2.277E−19 3 3.709E−15 −6.799E−17 2.662E−18 6.812E−19−1.743E−20 4 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 Lenssurface number:2 n\m 0 1 2 3 4 5 0 0.000E+00 −5.773E−02 0.000E+009.930E−06 −1.400E−06 8.729E−10 1 0.000E+00 9.210E−06 −5.513E−079.645E−09 2.147E−09 −6.202E−11 2 −7.640E−05 2.354E−07 −1.560E−074.035E−09 1.621E−10 −1.762E−12 3 4.933E−06 −5.752E−08 6.152E−09−1.080E−10 −1.475E−11 3.831E−13 4 −1.006E−07 2.187E−09 −5.144E−11−4.375E−12 1.582E−13 0.000E+00 n\m 6 7 8 9 10 0 −1.094E−10 1.100E−12−8.609E−15 −6.903E−17 6.609E−18 1 1.749E−12 −5.472E−14 2.144E−16−4.280E−18 7.170E−19 2 −7.529E−14 −3.309E−15 3.333E−17 8.481E−192.378E−20 3 6.674E−15 8.053E−17 −5.512E−18 −1.980E−19 3.169E−21 40.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 Lens surface number:3n\m 0 1 2 3 4 5 0 0.000E+00 2.050E−02 0.000E+00 −1.598E−06 −5.950E−087.905E−11 1 0.000E+00 −1.047E−05 1.804E−07 7.577E−11 1.019E−11 1.632E−142 −2.167E−06 −7.763E−09 4.831E−11 1.906E−12 1.717E−15 −4.322E−18 3−9.481E−10 2.209E−11 6.624E−13 6.194E−15 3.129E−17 −1.318E−19 41.245E−12 −3.925E−14 −4.635E−17 7.326E−18 −4.075E−20 0.000E+00 n\m 6 7 89 10 0 1.775E−12 1.901E−15 −5.836E−17 5.368E−20 −7.956E−22 1 −9.030E−163.189E−18 −5.694E−21 −1.892E−22 −1.522E−24 2 5.171E−19 −8.042E−21−6.550E−23 1.493E−24 −3.972E−27 3 6.017E−21 −1.174E−23 2.359E−26−1.154E−27 −6.743E−29 4 0.000E+00 0.000E+00 0.000E+00 0.000E+000.000E+00 Lens surface number:4 n\m 0 1 2 3 4 5 0 0.000E+00 9.490E−030.000E+00 −1.722E−06 −3.383E−08 9.478E−11 1 0.000E+00 −8.357E−069.769E−08 −2.265E−10 5.880E−12 3.231E−14 2 −2.646E−06 −7.779E−095.986E−11 1.912E−12 3.761E−16 −1.144E−16 3 1.400E−09 1.600E−11 4.824E−135.345E−15 6.171E−17 4.352E−19 4 −1.140E−11 −3.129E−14 2.926E−165.694E−18 4.522E−20 0.000E+00 n\m 6 7 8 9 10 0 4.805E−13 −2.678E−162.751E−18 2.274E−19 −3.174E−21 1 8.972E−18 7.329E−19 −5.795E−209.604E−23 −2.010E−24 2 3.245E−19 1.428E−20 2.269E−24 4.105E−25−8.401E−27 3 −7.626E−22 2.707E−24 2.018E−26 −7.895E−27 −2.122E−30 40.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00

FIGS. 44 to 46 are graphs showing a state that the laser beams LM isimage-formed by a post-deflection optical system 721 to which theoptical characteristics of Tables 6 and 7 are provided. Similar to thecase explained in FIGS. 10 to 12, each graph shows that the first imageforming lens 730 a or the second image forming lens 730 b, or bothlenses are intentionally detached, so that the image formingcharacteristic is improved. The specific explanation of each of thelaser beams LB, LY, and LC is omitted since the results, which aresimilar to the second embodiment shown in FIGS. 13 to 15 and FIGS. 16 to18, can be obtained.

FIG. 44 is a graph showing the relationship between an amount of defocus(change of image-formation position) of the main scanning direction andthe position of the main scanning direction in a state that the imageforming lenses 730 are detached in connection with the laser beams LM(LMa and LMb are arrayed to have a predetermined distance in thesub-scanning direction). In this case, a curve FSY0 shows that each offirst and second image forming lenses 730 a and 730 b is detached. Acurve FSY1 shows that only the second image forming lens 630 b isdetached (only the first image forming lens 730 a is used). A curve FSY2corresponds to a state that each of the first and second lenses 730 aand 730 b is set.

FIG. 45 is a graph showing the relationship between an amount of defocusof the sub-scanning direction and the position of the main scanningdirection in a state that the image-forming lens is detached inconnection with the laser beams LM.

In this case, a curve FSZ0 shows that each of first and second imageforming lenses 730 a and 730 b is detached. A curve FSZ1 shows that onlythe second image forming lens 730 b is detached (only the first imageforming lens 730 a is used). A curve FSZ2 corresponds to a state thateach of the first and second lenses 730 a and 730 b is set.

FIG. 46 is a graph showing the relationship between an amount of a beamposition correction, which includes a difference between an actualposition of the image forming in the main scanning direction and alogical position of the image formation, and the position of the mainscanning direction in connection with the laser beams LY. In this case,a curve Y0 shows that each of first and second image forming lenses 730a and 730 b is detached. A curve Y1 shows that only the second imageforming lens 730 b is detached (only the first image forming lens 730 ais used). A curve Y2 corresponds to a state that each of the first andsecond lenses 730 a and 730 b is set.

As shown in FIG. 44, if each of first and second image forming lenses730 a and 730 b is detached, the laser beam emitted from the lightsource is image-formed on a portion further than the image surface withrespect to the main scanning direction by the pre-deflection opticalsystem 707 (FSY0). If only the first image forming lens 730 a isinserted, the laser beam, which passes through a portion close to thecenter of the image forming lens 730 a, is image-formed on a portionclose to the polygon mirror unit 5 than FY0. The laser beam, whichpasses through a portion close the end portion of the image forming lens730 a, is image-formed on a portion opposite to the polygon mirror unit5 than FSY0. In other words, at the portion close to the center of thelens, the first image forming lens 730 a has power with which the imageforming position of the main scanning direction can be moved to thepolygon mirror unit. At the portion close to the end portion of thelens, the first image forming lens 730 a has a function of moving theimage forming position to the portion opposite to the polygon mirrorunit (FSY1).

If the second image forming lens 730 b is set, the laser beam, whichpasses through a portion close to the center of the image forming lens730 a, and the laser beam, which passes through a portion close the endportion of the image forming lens 730 a, are substantially linearlyimage-formed on a predetermined image surface, respectively. In otherwords, at the portion close to the center of the lens, the second imageforming lens 730 b has power with which the image forming position ofthe main scanning direction can be moved to a portion to the polygonmirror unit. At the portion close to the end portion of the lens, thesecond image forming lens 730 b has a greater function of moving theimage forming position to the polygon mirror unit. In other words, thesecond image forming lens 730 b is formed to have power, which isincreased as the lens 730 b is away from the center of the lens withrespect to the main scanning direction (FSY2). Thereby, even if thetemperature and humidity are changed, there can be provided thepost-deflection optical system having little change of the image formingposition.

As shown in FIG. 45, if the first and second image forming lenses 730 aand 730 b of the post-deflection optical system 721 are intentionallydetached, the laser beams emitted from the light sources areimage-formed on a portion close to the reflection point of eachreflection surface of the polygon mirror body 5 a with respect to thesub-scanning direction perpendicular to the main scanning direction(FSZ0). At this time, if only the first image forming lens 730 a isinserted, the laser beam, which is passed through substantially thecenter of the lens, is image-formed on a portion much closer to thepre-deflection optical system than the reflection point of each of thereflection surface of the polygon mirror body 5 a. In other words, thefirst image forming lens 730 a has a function of moving the imageforming position to the direction, which is further than the imagesurface. The amount of the movement of the image forming position of thesub-scanning direction becomes large at the central portion of the lensas compared with the end portion of the lens (FSZ1). Moreover, by theinsertion of the second image forming lens 730 b, the laser beam, whichis passed through the center of the first image forming lens, and thelaser beam, which is passed through the end portion of the lend, aresubstantially linearly image-formed on a predetermined image surface,respectively. In other word, the second image lens 730 b has power withwhich the image forming position of the sub-scanning direction can bemoved to the image surface side in the entire area of the main scanningdirection of the lens. That is, power of the second image forming lens730 b of the sub-scanning direction in the central area of the lens isset to be smaller than the lens end portion (FSZ2). Thereby, even if theamount of correcting inclination of each reflection surface of thepolygon mirror body 5 a is large and the temperature and humidity arechanged, post-deflection optical system having little change of theimage forming position can be provided.

As shown in FIG. 46, if the first and second image forming lenses 730 aand 730 b of the post-deflection optical system are intentionallydetached, the laser beams, which are emitted from the light sources, andwhich are passed through the position corresponding to the center of thelens in the case in which the image forming lens 730 exists, areimage-formed on a predetermined image surface (Y0). In this case, ifonly the first image forming lens 730 a is inserted, the laser beam,which is passed through the center of the lens, is image-formed atsubstantially the equal position with respect to the main scanningdirection of the lens. Then, the laser beam, which is passed through thelens end portion, is shifted to the center of the lens so as to beimage-formed in proportion to the distance between the position of themain scanning direction where the laser beams are passed and the centerof the main scanning direction of the lens (Y1). Also, if the secondimage forming lens 730 b is further inserted, the laser beam, which ispassed through the center of the lens, is image-formed at substantiallythe equal position with respect to the main scanning direction of thelens. Then, the laser beam, which is passed through the lens endportion, is further shifted to the center of the lens so as to beimage-formed in proportion to the distance between the position of themain scanning direction where the laser beams are passed and the centerof the main scanning direction of the lens (Y2). In other words, thefirst and second image forming lenses 730 a and 730 b have the functionof moving the laser beam to the center of the main scanning directionwith respect to the main scanning direction as the distance of the mainscanning direction from the center of the lens is increased. Thefunction of moving the laser beam is increased by a predeterminedfunction as the distance of the main scanning direction from the centerof the lens is increased. Therefore, there can be obtained a goodconstant velocity in deflecting the laser beam in the main scanningdirection. Also, the variation of the position of the main scanningdirection caused by the change of the temperature and humidity can bereduced.

As explained above, the optical characteristics of Tables 6 and 7 aregiven to the image forming lens 730 of the multi-beam exposer unit 701including the optical elements similar to the multi-beam exposer unit ofFIGS. 2 and 3. Thereby, as explained with reference to FIGS. 44 to 46,there can be provided the post-deflection optical system in which theamount of defocus of the main scanning direction, that of thesub-scanning direction, and the position of the laser beam of the mainscanning direction are not changed by depending on the variations of thetemperature and humidity even if two plastic lenses are used.

The first and second image forming lenses 730 a and 730 b are placed atthe position, which is defined such that the distance from thereflection point of each reflection surface of the polygon mirror body 5a is shorter than the distance from the image surface, that is, theportion close to the polygon mirror unit 5 than the center of thedistance between each reflection point of each reflection surface of thepolygon mirror body 5 a and the image surface. As a result, the size ofthe multi-beam exposer unit can be reduced.

As explained above, according to the multi-beam exposer unit of thisinvention, the absolute value of the coma aberration, which is generatedby the half mirror, can be reduced by placing the parallel plate, whichis inclined to be opposite to the direction where the half mirror isinclined, in the optical path between the light source and the opticalpath of the polygon mirror. In other words, it is assumed that the comaaberration, which is generated when a certain beam passes through i-thhalf mirror, is Fi, and that the beam passes through a (i=1 to a) halfmirrors in all.

The beam is made incident on the parallel plate with a thickness tg,which satisfies the following equation, at an incident angle ug.

−tg×ug ³×(ng ²−1)/ng ³=−(F 1+F 2+ . . . Fa)

Thereby, the coma aberration can be canceled.

On the other hand, in order to make the number of the parallel plates,there can be considered a method in which the absolute values of thecoma aberration of the laser beam whose coma aberration is maximum andthe laser beam whose coma aberration is minimum are set to be the same.

For example, it is assumed that the laser beam whose coma aberration ismaximum is shown by (F1+F2+ . . . +Fa) and that the coma aberration ofthe laser beam whose coma aberration is minimum is 0.

The beam is made incident on the parallel plate with a thickness tg,which satisfies the following equation, at an incident angle ug.

−tg×ug ³×(ng ²−1)/ng ³=−(F 1+F 2+ . . . +Fa)/2

As is obvious from the maximum absolute value of the coma aberration of(F1+F2+ . . . Fa)/2, this can be set to the half of the case in which noparallel plate exists.

It is assumed that the coma aberration generated by the half mirror isF1.

The beam is made incident on the parallel plate with a thickness tg,which satisfies the following equation, at an incident angle ug.

−tg×ug ³×(ng ²−1)/ng ² =−F 1/2

As is obvious from the maximum absolute value of the coma aberration ofF1/2, this can be set to the half of the case in which no parallel plateexists.

The parallel plate is formed to be integral with the dust preventionglass, which prevents dust from being adhered around the polygon mirror.As a result, the wind loss of each reflection surface of the polygonmirror, the generation of noise, and adhesion of undesirable dust ontoeach reflection surface can be prevented.

Additional advantages and modifications will readily occur to thoseskilled in the art. Therefore, the invention in its broader aspects isnot limited to the specific details and representative embodiments shownand described herein. Accordingly, various modifications may be madewithout departing from the spirit or scope of the general inventiveconcept as defined by the appended claims and their equivalent.

What is claimed is:
 1. A multi-beam exposure unit comprising: M sets oflight sources for emitting Ni light beams wherein at least one set ofthe light sources satisfies Ni (i=1, 2, 3, or 4)≧1, wherein M is apositive integer=1, 2, 3, or 4, and i is a positive integer no greaterthan M; first optical means having M sets of optical members, havingpositive power and a larger absolute value of power in a sub-scanningdirection than in a main-scanning direction, the sub-scanning directionbeing perpendicular to the main-scanning direction, for converging thebeam in the sub-scanning direction, and M−1 synthesizing reflectionmirrors for reflecting M−1 groups of beams from M−1 sets of opticalmembers so that the M groups of beams are substantially overlaid on eachother in the main-scanning direction; deflecting means, having rotatablereflection surfaces, for deflecting light in the main-scanningdirection; and second optical means having a set of lenses for imageforming $\sum\limits_{i = 1}^{M}{Ni}$

 beams on a predetermined image surface at equal speed, and forcorrecting an inclination of the reflection surfaces of the deflectingmeans with respect to an axis of rotation of the deflecting means,wherein each of the lenses is positioned such that a distance from areflection point on the deflecting means is shorter than a distance fromthe image surface, and wherein one lens that is placed on a side of thedeflecting means moves an image forming position of the main scanningdirection to the side of the deflecting means at a position close to thecenter of the lens, and moves the image forming position of the mainscanning direction to a side opposite to the deflecting means at aposition close to both end portions of the lens.
 2. A multi-beamexposure unit comprising: M sets of light sources for emitting Ni lightbeams wherein at least one set of the light sources satisfies Ni (i=1,2, 3, or 4)≧1, wherein M is a positive integer=1, 2, 3, or 4, and i is apositive integer no greater than M; first optical means including M setsof optical members, having positive power and a larger absolute value ofpower in a sub-scanning direction than in a main-scanning direction, thesub-scanning direction being perpendicular to the main-scanningdirection, for converging the beam in the sub-scanning direction, andM−1 synthesizing reflection mirrors for reflecting M−1 groups of beamsfrom M−1 sets of optical members so that the M groups of beams aresubstantially overlaid on each other in the main-scanning direction;deflecting means, having rotatable reflection surfaces, for deflectinglight in the main-scanning direction; second optical means having a setof lenses for image forming $\sum\limits_{i = 1}^{M}{Ni}$

 beams on a predetermined image surface at equal speed, and forcorrecting an inclination of the reflection surfaces of the deflectingmeans with respect to an axis of rotation of the deflecting means,wherein each of the lenses is positioned to include an image formingcharacteristic such that a distance from a reflection point on thedeflecting means is shorter than a distance from the image surface, andwherein one lens placed on the side of the deflecting means moves animage forming position of the main scanning direction and an imageforming position of a perpendicular direction to the side of thedeflecting means at a position close to the center of the lens.
 3. Amulti-beam exposure unit comprising: M sets of light sources foremitting Ni light beams wherein at least one set of the light sourcessatisfies Ni (i=1, 2, 3, or 4)≧2, wherein M is a positive integer=1, 2,3, or 4, and i is a positive integer no greater than M; first opticalmeans including M sets of optical members, having positive power and alarger absolute value of power in a sub-scanning direction than in amain-scanning direction, the sub-scanning direction being perpendicularto the main-scanning direction, for converging the beam in thesub-scanning direction, and M−1 synthesizing reflection mirrors forreflecting M−1 groups of beams from M−1 sets of optical members so thatthe M groups of beams are substantially overlaid on each other in themain-scanning direction; deflecting means, having rotatable reflectionsurfaces, for deflecting light in the main-scanning direction; andsecond optical means having a set of lenses for image forming$\sum\limits_{i = 1}^{M}{Ni}$

 beams on a predetermined image surface at equal speed and forcorrecting an inclination of the reflection surfaces of the deflectingmeans with respect to an axis of rotation of the deflecting means,wherein each of the lenses is positioned to include an image formingcharacteristic such that a distance from a reflection point on thedeflecting means is shorter than a distance from the image surface, andwherein one lens that is placed on a side of the deflecting means movesa beam position of the main scanning direction to an optical axis at aposition close to a lens end portion, and another lens placed on theside of the image surface has a function of further moving the beamposition of the main scanning direction to the optical axis at aposition close to the lens end portion.
 4. A multi-beam exposure unitcomprising: M sets of light sources for emitting Ni light beams whereinat least one set of the light sources satisfies Ni (i=1, 2, 3, or 4)≧1,wherein M is a positive integer=1, 2, 3, or 4, and i is a positiveinteger no greater than M; first optical means having M sets of opticalmembers, having positive power and a larger absolute value of power in asub-scanning direction than in a main-scanning direction, thesub-scanning direction being perpendicular to the main-scanningdirection, for converging the beam in the sub-scanning direction, anddeflecting means, having rotatable reflection surfaces, for deflectinglight in the main-scanning direction; and second optical means having aset of lenses for image forming $\sum\limits_{i = 1}^{M}{Ni}$

 beams on a predetermined image surface at equal speed, and forcorrecting an inclination of the reflection surfaces of the deflectingmeans with respect to an axis of rotation of the deflecting means,wherein each of the lenses is positioned such that a distance from areflection point on the deflecting means is shorter than a distance fromthe image surface, and wherein one lens that is placed on a side of thedeflecting means moves an image forming position of the main scanningdirection to the side of the deflecting means at a position close to thecenter of the lens, and moves the image forming position of the mainscanning direction to a side opposite to the deflecting means at aposition close to both end portions of the lens.
 5. A multi-beamexposure unit comprising: M sets of light sources for emitting Ni lightbeams wherein at least one set of the light sources satisfies Ni (i=1,2, 3, or 4)≧1, wherein M is a positive integer=1, 2, 3, or 4, and i is apositive integer no greater than M; first optical means including M setsof optical members, having positive power and a larger absolute value ofpower in a sub-scanning direction than in a main-scanning direction, thesub-scanning direction being perpendicular to the main-scanningdirection, for converging the beam in the sub-scanning direction, anddeflecting means, having rotatable reflection surfaces, for deflectinglight in the main-scanning direction; second optical means having a setof lenses for image forming $\sum\limits_{i = 1}^{M}{Ni}$

 beams on a predetermined image surface at equal speed, and forcorrecting an inclination of the reflection surfaces of the deflectingmeans with respect to an axis of rotation of the deflecting means,wherein each of the lenses is positioned to include an image formingcharacteristic such that a distance from a reflection point on thedeflecting means is shorter than a distance from the image surface, andwherein one lens placed on the side of the deflecting means moves animage forming position of the main scanning direction and an imageforming position of a perpendicular direction to the side of thedeflecting means at a position close to the center of the lens.
 6. Amulti-beam exposure unit comprising: M sets of light sources foremitting Ni light beams wherein at least one set of the light sourcessatisfies Ni (i=1, 2, 3, or 4)≧2, wherein M is a positive integer=1, 2,3, or 4, and i is a positive integer no greater than M; first opticalmeans including M sets of optical members, having positive power and alarger absolute value of power in a sub-scanning direction than in amain-scanning direction, the sub-scanning direction being perpendicularto the main-scanning direction, for converging the beam in thesub-scanning direction, and deflecting means, having rotatablereflection surfaces, for deflecting light in the main-scanningdirection; and second optical means having a set of lenses for imageforming $\sum\limits_{i = 1}^{M}{Ni}$

 beams on a predetermined image surface at equal speed and forcorrecting an inclination of the reflection surfaces of the deflectingmeans with respect to an axis of rotation of the deflecting means,wherein each of the lenses is positioned to include an image formingcharacteristic such that a distance from a reflection point on thedeflecting means is shorter than a distance from the image surface, andwherein one lens that is placed on a side of the deflecting means movesa beam position of the main scanning direction to an optical axis at aposition close to a lens end portion, and another lens placed on theside of the image surface has a function of further moving the beamposition of the main scanning direction to the optical axis at aposition close to the lens end portion.
 7. A beam exposure unitcomprising: a light source for emitting a light beam; first opticalmeans having a first lens for converting a light beam emitted from therespective light source to non-divergent light, an optical member,having positive power and a larger absolute value of power in asub-scanning direction than in a main-scanning direction, thesub-scanning direction being perpendicular to the main-scanningdirection, for converging the beam in the sub-scanning direction,deflecting means, having rotatable reflection surfaces, for deflectinglight in the main-scanning direction; and second optical means having aset of lenses for image forming a beam on a predetermined image surfaceat equal speed, and for correcting an inclination of the reflectionsurfaces of the deflecting means with respect to an axis of rotation ofthe deflecting means, wherein each of the lenses is positioned such thata distance from a reflection point on the deflecting means is shorterthan a distance from the image surface, and wherein one lens that isplaced on a side of the deflecting means moves an image forming positionof the main scanning direction to the side of the deflecting means at aposition close to the center of the lens, and moves the image formingposition of the main scanning direction to a side opposite to thedeflecting means at a position close to both end portions of the lens.8. A beam exposure unit comprising: a light source for emitting a lightbeam; first optical means including an optical member, having positivepower and a larger absolute value of power in a sub-scanning directionthan in a main-scanning direction, the sub-scanning direction beingperpendicular to the main-scanning direction, for converging the beam inthe sub-scanning direction, deflecting means, having rotatablereflection surfaces, for deflecting light in the main-scanningdirection; and second optical means having a set of lenses for imageforming a beam on a predetermined image surface at equal speed, and forcorrecting an inclination of the reflection surfaces of the deflectingmeans with respect to an axis of rotation of the deflecting means,wherein each of the lenses is positioned to include an image formingcharacteristic such that a distance from a reflection point on thedeflecting means is shorter than a distance from the image surface, andwherein one lens placed on the side of the deflecting means moves animage forming position of the main scanning direction and an imageforming position of a perpendicular direction to the side of thedeflecting means at a position close to the center of the lens.